The structure of pro-lie groups:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, Germany
EMS Press
[2023]
|
| Edition: | Second edition |
| Series: | EMS Tracts in mathematics
36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxii, 818 Seiten 23.5 cm x 16.5 cm |
| ISBN: | 3985470480 9783985470488 |
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MARC
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| 001 | BV049579692 | ||
| 003 | DE-604 | ||
| 005 | 20240412 | ||
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| 008 | 240221s2023 gw |||| 00||| eng d | ||
| 015 | |a 23,N51 |2 dnb | ||
| 016 | 7 | |a 1312932678 |2 DE-101 | |
| 020 | |a 3985470480 |9 3-98547-048-0 | ||
| 020 | |a 9783985470488 |c hbk: EUR 119.00 (DE), EUR 122.40 (AT) |9 978-3-98547-048-8 | ||
| 024 | 3 | |a 9783985470488 | |
| 035 | |a (OCoLC)1415292649 | ||
| 035 | |a (DE-599)DNB1312932678 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-29T | ||
| 084 | |8 1\p |a 510 |2 23sdnb | ||
| 100 | 1 | |a Hofmann, Karl H. |d 1932- |e Verfasser |0 (DE-588)115780734 |4 aut | |
| 245 | 1 | 0 | |a The structure of pro-lie groups |c Karl H. Hofmann, Sidney A. Morris |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin, Germany |b EMS Press |c [2023] | |
| 300 | |a xxii, 818 Seiten |c 23.5 cm x 16.5 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a EMS Tracts in mathematics |v 36 | |
| 653 | |a Lie theory of connected and almost connected pro-Lie groups | ||
| 653 | |a completenes | ||
| 653 | |a exponential function | ||
| 653 | |a local Iwasawa splitting | ||
| 653 | |a open mapping theorems Levi–Malcev splitting | ||
| 653 | |a pro-Lie algebras | ||
| 653 | |a pro-Lie groups | ||
| 653 | |a quotient groups | ||
| 653 | |a structure theory of locally compact groups | ||
| 700 | 1 | |a Morris, Sidney A. |d 1947- |e Verfasser |0 (DE-588)132019515 |4 aut | |
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-98547-548-3 |
| 780 | 0 | 0 | |i Vorangegangen ist |z 978-3-03719-032-6 |
| 830 | 0 | |a EMS Tracts in mathematics |v 36 |w (DE-604)BV022480257 |9 36 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034924633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a vlb |d 20231211 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Record in the Search Index
| _version_ | 1805071313812848640 |
|---|---|
| adam_text |
CONTENTS
FOREWORD
.
V
PREFACE
TO
THE
SECOND
EDITION
.
VII
PREFACE
TO THE
FIRST
EDITION
.
XI
STRUCTURE
OF
COMPACT
GROUPS
AND
PRO-LIE
GROUPS:
OUR
SELECTION
.
1
COMPACT
ABELIAN
GROUPS
.
3
COMPACT
GROUPS
.
6
LIE
THEORY
.
11
ABELIAN
PRO-LIE
GROUPS
.
13
PRO-LIE
GROUPS
.
14
1
LIE
GROUPS
AND
THE
LIE
THEORY
OF
TOPOLOGICAL
GROUPS
.
17
THE
GENERAL
DEFINITION
OF
ALIE
GROUP
.
17
THE
EXPONENTIAL
FUNCTION
OF
TOPOLOGICAL
GROUPS
.
20
THE
LIE
ALGEBRA
OF
A
TOPOLOGICAL
GROUP
.
25
THE
CATEGORY
OF
TOPOLOGICAL
GROUPS
WITH
LIE
ALGEBRAS
.
30
THE
LIE
ALGEBRA
FUNCTOR
HAS
A
LEFT
ADJOINT
FUNCTOR
.
38
SOPHUS
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
.
42
THE
ADJOINT
REPRESENTATION
OF
A
TOPOLOGICAL
GROUP
WITH
A
LIE
ALGEBRA
.
42
POSTSCRIPT
.
45
2
PRO-LIE
GROUPS
.
47
PROJECTIVE
LIMITS
OF
LIE
GROUPS
.
47
THE
LIE
ALGEBRAS
OF
PROJECTIVE
LIMITS
OF
LIE
GROUPS
.50
PRO-LIE
ALGEBRAS
.
50
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
AND
LIE
ALGEBRAS
.
55
PRO-LIE
GROUPS
.
61
SOME
EXAMPLES
.
80
AN
OVERVIEW
OF
THE
DEFINITIONS
OF
A
PRO-LIE
GROUP
.
80
POSTSCRIPT
.
84
3
QUOTIENTS
OF
PRO-LIE
GROUPS
.
89
QUOTIENT
OBJECTS
IN
CATEGORIES
.
90
QUOTIENT
GROUPS
OF
PRO-LIE
GROUPS
.
91
XVIII
CONTENTS
THE
ONE-PARAMETER
SUBGROUP
LIFTING
LEMMA
.
94
SUFFICIENT
CONDITIONS
FOR
QUOTIENTS
TO
BE
COMPLETE
.
105
QUOTIENT
MAPS
BETWEEN
PRO-LIE
GROUPS
.
120
POSTSCRIPT
.
123
4
ABELIAN
PRO-LIE
GROUPS
.
125
EXAMPLES
OF
ABELIAN
PRO-LIE
GROUPS
.
125
WEIL
'
S
LEMMA
.
129
VECTOR
GROUP
SPLITTING
THEOREMS
.
133
COMPACTLY
GENERATED
ABELIAN
PRO-LIE
GROUPS
.
147
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
REVISITED
.
150
THE
DUALITY
THEORY
OF
ABELIAN
PRO-LIE
GROUPS
.
153
THE
TORAL
HOMOMORPHIC
IMAGES
OF
AN
ABELIAN
PRO-LIE
GROUP
.
157
THE
EXPONENTIAL
FUNCTION
OF
COMPACT
ABELIAN
GROUPS
AND
QUOTIENT
MORPHISMS
.
161
POSTSCRIPT
.
172
5
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
.
175
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
FOR
PRO-LIE
GROUPS
.
175
SEMIDIRECT
PRODUCTS
.
191
POSTSCRIPT
.
194
6
PROFINITE-DIMENSIONAL
MODULES
AND
LIE
ALGEBRAS
.
197
MODULES
OVER
A
LIE
ALGEBRA
.
197
DUALITY
OF
MODULES
.200
SEMISIMPLE
AND
REDUCTIVE
MODULES
.
206
REDUCTIVE
PRO-LIE
ALGEBRAS
.
211
TRANSFINITELY
SOLVABLE
LIE
ALGEBRAS
.
214
THE
RADICAL
AND
LEVI-MAL
'
CEV:
EXISTENCE
.
221
TRANSFINITELY
NILPOTENT
LIE
ALGEBRAS
.
227
THE
NILPOTENT
RADICALS
.
231
SPECIAL
ENDOMORPHISMS
OF
PRO-LIE
ALGEBRAS
.
237
LEVI-MAL
'
CEV:
UNIQUENESS
.
241
DIRECT
AND
SEMIDIRECT
SUMS
REVISITED
.
245
CARTAN
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
247
THEOREM
OF
ADO
.
264
THE
AUTOMORPHISM
GROUP
OF
SEMISIMPLE
PRO-LIE
ALGEBRAS
.
266
POSTSCRIPT
.282
CONTENTS
XIX
7
THE
STRUCTURE
OF
SIMPLY
CONNECTED
PRO-LIE
GROUPS
.
285
THE
ADJOINT
ACTION
.
285
SIMPLY
CONNECTED
PRONILPOTENT
PRO-LIE
GROUPS
.286
THE
TOPOLOGICAL
SPLITTING
TECHNIQUE
.
290
SIMPLE
CONNECTIVITY
.
293
UNIVERSAL
MORPHISM
VERSUS
UNIVERSAL
COVERING
MORPHISM
.
303
POSTSCRIPT
.
305
8
ANALYTIC
SUBGROUPS
AND
THE
LIE
THEORY
OF
PRO-LIE
GROUPS
.
307
THE
EXPONENTIAL
FUNCTION
ON
THE
INNER
DERIVATION
ALGEBRA
.
307
ANALYTIC
SUBGROUPS
.
311
AUTOMORPHISMS
AND
INVARIANT
ANALYTIC
SUBGROUPS
.
321
CENTRALIZERS
.
322
NORMALIZERS
.
325
SUBALGEBRAS
AND
SUBGROUPS
.
327
THE
CENTER
.
329
THE
COMMUTATOR
SUBGROUP
.
329
FINITE-DIMENSIONAL
CONNECTED
PRO-LIE
GROUPS
.
338
COMPACT
CENTRAL
SUBGROUPS
.
356
DIVISIBILITY
OF
GROUPS
AND
CONNECTED
PRO-LIE
GROUPS
.
359
THE
OPEN
MAPPING
THEOREM
.
365
COMPLETING
PROTO-LIE
GROUPS
.
369
UNITARY
REPRESENTATIONS
.
371
POSTSCRIPT
.
372
9
THE
GLOBAL
STRUCTURE
OF
CONNECTED
PRO-LIE
GROUPS
.
375
SOLVABILITY
OF
PRO-LIE
GROUPS
.
376
THE
RADICAL
.
388
SEMI
SIMPLE
AND
REDUCTIVE
GROUPS
.392
NILPOTENCY
OF
PRO-LIE
GROUPS
.
402
THE
NILRADICAL
AND
THE
COREDUCTIVE
RADICAL
.
406
THE
STRUCTURE
OF
REDUCTIVE
PRO-LIE
GROUPS
.
412
POSTSCRIPT
.
419
10
SPLITTING
THEOREMS
FOR
PRO-LIE
GROUPS
.
423
SPLITTING
REDUCTIVE
GROUPS
SEMIDIRECTLY
.
424
VECTOR
GROUP
SPLITTING
IN
NONCOMMUTATIVE
GROUPS
.
436
THE
STRUCTURE
OF
PRONILPOTENT
AND
PROSOLVABLE
GROUPS
.
442
CONJUGACY
THEOREMS
.
451
POSTSCRIPT
.
454
XX
CONTENTS
11
PROCOMPACT
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
AND
COMPACT
SUBGROUPS
OF
PRO-LIE
GROUPS
.
457
PROCOMPACT
MODULES
AND
LIE
ALGEBRAS
.
457
PROCOMPACT
LIE
ALGEBRAS
AND
COMPACTLY
EMBEDDED
LIE
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
464
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
469
CONJUGACY
OF
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
.
472
COMPACT
CONNECTED
GROUPS
.
483
COMPACT
SUBGROUPS
.485
POTENTIALLY
COMPACT
PRO-LIE
GROUPS
.
488
THE
CONJUGACY
OF
MAXIMAL
COMPACT
CONNECTED
SUBGROUPS
.
491
THE
ANALYTIC
SUBGROUPS
HAVING
A
FULL
LIE
ALGEBRA
.
500
MAXIMAL
COMPACT
SUBGROUPS
OF
CONNECTED
PRO-LIE
GROUPS
.
512
AN
ALTERNATIVE
OPEN
MAPPING
THEOREM
.
517
ON
THE
CENTER
OF
A
CONNECTED
PRO-LIE
GROUP
.
519
POSTSCRIPT
.
522
12
THE
STRUCTURE
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
527
THE
AUTOMORPHISM
GROUPS
OF
SEMISIMPLE
PRO-LIE
GROUPS
.
527
TOPOLOGICAL
GROUPS
WITH
PRO-LIE
IDENTITY
COMPONENT
.
534
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
538
MAXIMAL
COMPACT
SUBGROUPS
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
540
THE
CONJUGACY
OF
MAXIMAL
COMPACT
SUBGROUPS
IN
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
543
THE
STRUCTURE
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
544
POSTSCRIPT
.
544
13
ALMOST
CONNECTED
PRO-LIE
GROUPS
AND
THEIR
TOPOLOGY
.
547
ALMOST
CONNECTED
PRO-LIE
GROUPS
AND
THEIR
TOPOLOGY
.
547
POSTSCRIPT
.
556
14
IWASAWA
'
S
LOCAL
SPLITTING
THEOREM
.
557
LOCALLY
SPLITTING
LIE
GROUP
QUOTIENTS
OF
PRO-LIE
GROUPS
.557
THE
LIE
ALGEBRA
THEORY
OF
THE
LOCAL
SPLITTING
.
562
SPLITTING
ON
THE
GROUP
LEVEL
.
571
SOME
COMMENTS
ON
CONNECTEDNESS
.
576
POSTSCRIPT
.
577
15
CATALOG
OF
EXAMPLES
.
579
CLASSIFICATION
OF
THE
EXAMPLES
IN
THE
CATALOG
.
579
ABELIAN
PRO-LIE
GROUPS
.580
CONTENTS
XXI
A
SIMPLE
CONSTRUCTION
.
588
PRONILPOTENT
PRO-LIE
GROUPS
.
591
PROSOLVABLE
PRO-LIE
GROUPS
.
595
SEMISIMPLE
AND
REDUCTIVE
PRO-LIE
GROUPS
.
602
MIXED
GROUPS
.609
EXAMPLES
CONCERNING
THE
DEFINITION
OF
LIE
AND
PRO-LIE
GROUPS
.
611
ANALYTIC
SUBGROUPS
OF
PRO-LIE
GROUPS
.
615
EXAMPLES
CONCERNING
SIMPLE
CONNECTIVITY
.
616
EXAMPLE
CONCERNING
G-MODULE
THEORY
.
617
POSTSCRIPT
.
617
PANORAMIC
OVERVIEW
OF
THIS
BOOK
.
619
PART
1.
THE
BASE
THEORY
OF
PRO-LIE
GROUPS
.
625
PART
2.
THE
ALGEBRA
OF
PRO-LIE
ALGEBRAS
.
639
PART
3.
THE
FINE
LIE
THEORY
OF
PRO-LIE
GROUPS
.
648
PART
4.
GLOBAL
STRUCTURE
THEORY
OF
CONNECTED
PRO-LIE
GROUPS
.
656
PART
5.
THE
ROLE
OF
COMPACTNESS
ON
THE
PRO-LIE
ALGEBRA
LEVEL
.
667
PART
6.
THE
ROLE
OF
COMPACT
SUBGROUPS
OF
PRO-LIE
GROUPS
.
675
PART
7.
LOCAL
SPLITTING
ACCORDING
TO
IWASAWA
.
686
A1
LIMITS
OF
TOPOLOGICAL
GROUPS
.
689
LIMITS
.
690
THE
EXTERNAL
APPROACH
TO
PROJECTIVE
LIMITS
.
704
PROJECTIVE
LIMITS
AND
LOCAL
COMPACTNESS
.709
THE
FUNDAMENTAL
THEOREM
ON
PROJECTIVE
LIMITS
.
716
THE
INTERNAL
APPROACH
TO
PROJECTIVE
LIMITS
.
719
PROJECTIVE
LIMITS
AND
COMPLETENESS
.
722
THE
CLOSED
SUBGROUP
THEOREM
.
725
THE
ROLE
OF
LOCAL
COMPACTNESS
.
729
THE
ROLE
OF
CLOSED
FULL
SUBCATEGORIES
IN
COMPLETE
CATEGORIES
.
731
POSTSCRIPT
.
734
A2
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.737
CHARACTER
GROUPS
OF
TOPOLOGICAL
VECTOR
SPACES
.
737
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
745
DUALITY
AT
WORK
FOR
THE
STRUCTURE
THEORY
OF
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
751
TOPOLOGICAL
PROPERTIES
OF
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
.
.
755
SUMMABILITY
IN
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
758
CONTINUOUS
SYMPLECTIC
MAPS
ON
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.758
XXII
CONTENTS
TENSOR
PRODUCTS
.
761
WEAKLY
COMPLETE
UNITAL
ALGEBRAS
.
762
THE
EXPONENTIAL
FUNCTION
.
766
WEAKLY
COMPLETE
SYMMETRIC
HOPF
ALGEBRAS
.
768
THE
SIGNIFICANCE
OF
GROUPLIKE
ELEMENTS
.
770
THE
SIGNIFICANCE
OF
PRIMITIVE
ELEMENTS
.
774
POSTSCRIPT
.
782
A3
THE
CAMPBELL-HAUSDORFF
FORMALISM
.785
POSTSCRIPT
.789
A4
VARIOUS
PIECES
OF
INFORMATION
ON
SEMISIMPLE
LIE
ALGEBRAS
.
791
BRACKETS
IN
SEMISIMPLE
LIE
ALGEBRAS
.
791
BRACKETS
IN
COMPACT
LIE
ALGEBRAS
.
792
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
.
794
POSTSCRIPT
.
795
REFERENCES
.797
INDEX
.
809 |
| adam_txt |
CONTENTS
FOREWORD
.
V
PREFACE
TO
THE
SECOND
EDITION
.
VII
PREFACE
TO THE
FIRST
EDITION
.
XI
STRUCTURE
OF
COMPACT
GROUPS
AND
PRO-LIE
GROUPS:
OUR
SELECTION
.
1
COMPACT
ABELIAN
GROUPS
.
3
COMPACT
GROUPS
.
6
LIE
THEORY
.
11
ABELIAN
PRO-LIE
GROUPS
.
13
PRO-LIE
GROUPS
.
14
1
LIE
GROUPS
AND
THE
LIE
THEORY
OF
TOPOLOGICAL
GROUPS
.
17
THE
GENERAL
DEFINITION
OF
ALIE
GROUP
.
17
THE
EXPONENTIAL
FUNCTION
OF
TOPOLOGICAL
GROUPS
.
20
THE
LIE
ALGEBRA
OF
A
TOPOLOGICAL
GROUP
.
25
THE
CATEGORY
OF
TOPOLOGICAL
GROUPS
WITH
LIE
ALGEBRAS
.
30
THE
LIE
ALGEBRA
FUNCTOR
HAS
A
LEFT
ADJOINT
FUNCTOR
.
38
SOPHUS
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
.
42
THE
ADJOINT
REPRESENTATION
OF
A
TOPOLOGICAL
GROUP
WITH
A
LIE
ALGEBRA
.
42
POSTSCRIPT
.
45
2
PRO-LIE
GROUPS
.
47
PROJECTIVE
LIMITS
OF
LIE
GROUPS
.
47
THE
LIE
ALGEBRAS
OF
PROJECTIVE
LIMITS
OF
LIE
GROUPS
.50
PRO-LIE
ALGEBRAS
.
50
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
AND
LIE
ALGEBRAS
.
55
PRO-LIE
GROUPS
.
61
SOME
EXAMPLES
.
80
AN
OVERVIEW
OF
THE
DEFINITIONS
OF
A
PRO-LIE
GROUP
.
80
POSTSCRIPT
.
84
3
QUOTIENTS
OF
PRO-LIE
GROUPS
.
89
QUOTIENT
OBJECTS
IN
CATEGORIES
.
90
QUOTIENT
GROUPS
OF
PRO-LIE
GROUPS
.
91
XVIII
CONTENTS
THE
ONE-PARAMETER
SUBGROUP
LIFTING
LEMMA
.
94
SUFFICIENT
CONDITIONS
FOR
QUOTIENTS
TO
BE
COMPLETE
.
105
QUOTIENT
MAPS
BETWEEN
PRO-LIE
GROUPS
.
120
POSTSCRIPT
.
123
4
ABELIAN
PRO-LIE
GROUPS
.
125
EXAMPLES
OF
ABELIAN
PRO-LIE
GROUPS
.
125
WEIL
'
S
LEMMA
.
129
VECTOR
GROUP
SPLITTING
THEOREMS
.
133
COMPACTLY
GENERATED
ABELIAN
PRO-LIE
GROUPS
.
147
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
REVISITED
.
150
THE
DUALITY
THEORY
OF
ABELIAN
PRO-LIE
GROUPS
.
153
THE
TORAL
HOMOMORPHIC
IMAGES
OF
AN
ABELIAN
PRO-LIE
GROUP
.
157
THE
EXPONENTIAL
FUNCTION
OF
COMPACT
ABELIAN
GROUPS
AND
QUOTIENT
MORPHISMS
.
161
POSTSCRIPT
.
172
5
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
.
175
LIE
'
S
THIRD
FUNDAMENTAL
THEOREM
FOR
PRO-LIE
GROUPS
.
175
SEMIDIRECT
PRODUCTS
.
191
POSTSCRIPT
.
194
6
PROFINITE-DIMENSIONAL
MODULES
AND
LIE
ALGEBRAS
.
197
MODULES
OVER
A
LIE
ALGEBRA
.
197
DUALITY
OF
MODULES
.200
SEMISIMPLE
AND
REDUCTIVE
MODULES
.
206
REDUCTIVE
PRO-LIE
ALGEBRAS
.
211
TRANSFINITELY
SOLVABLE
LIE
ALGEBRAS
.
214
THE
RADICAL
AND
LEVI-MAL
'
CEV:
EXISTENCE
.
221
TRANSFINITELY
NILPOTENT
LIE
ALGEBRAS
.
227
THE
NILPOTENT
RADICALS
.
231
SPECIAL
ENDOMORPHISMS
OF
PRO-LIE
ALGEBRAS
.
237
LEVI-MAL
'
CEV:
UNIQUENESS
.
241
DIRECT
AND
SEMIDIRECT
SUMS
REVISITED
.
245
CARTAN
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
247
THEOREM
OF
ADO
.
264
THE
AUTOMORPHISM
GROUP
OF
SEMISIMPLE
PRO-LIE
ALGEBRAS
.
266
POSTSCRIPT
.282
CONTENTS
XIX
7
THE
STRUCTURE
OF
SIMPLY
CONNECTED
PRO-LIE
GROUPS
.
285
THE
ADJOINT
ACTION
.
285
SIMPLY
CONNECTED
PRONILPOTENT
PRO-LIE
GROUPS
.286
THE
TOPOLOGICAL
SPLITTING
TECHNIQUE
.
290
SIMPLE
CONNECTIVITY
.
293
UNIVERSAL
MORPHISM
VERSUS
UNIVERSAL
COVERING
MORPHISM
.
303
POSTSCRIPT
.
305
8
ANALYTIC
SUBGROUPS
AND
THE
LIE
THEORY
OF
PRO-LIE
GROUPS
.
307
THE
EXPONENTIAL
FUNCTION
ON
THE
INNER
DERIVATION
ALGEBRA
.
307
ANALYTIC
SUBGROUPS
.
311
AUTOMORPHISMS
AND
INVARIANT
ANALYTIC
SUBGROUPS
.
321
CENTRALIZERS
.
322
NORMALIZERS
.
325
SUBALGEBRAS
AND
SUBGROUPS
.
327
THE
CENTER
.
329
THE
COMMUTATOR
SUBGROUP
.
329
FINITE-DIMENSIONAL
CONNECTED
PRO-LIE
GROUPS
.
338
COMPACT
CENTRAL
SUBGROUPS
.
356
DIVISIBILITY
OF
GROUPS
AND
CONNECTED
PRO-LIE
GROUPS
.
359
THE
OPEN
MAPPING
THEOREM
.
365
COMPLETING
PROTO-LIE
GROUPS
.
369
UNITARY
REPRESENTATIONS
.
371
POSTSCRIPT
.
372
9
THE
GLOBAL
STRUCTURE
OF
CONNECTED
PRO-LIE
GROUPS
.
375
SOLVABILITY
OF
PRO-LIE
GROUPS
.
376
THE
RADICAL
.
388
SEMI
SIMPLE
AND
REDUCTIVE
GROUPS
.392
NILPOTENCY
OF
PRO-LIE
GROUPS
.
402
THE
NILRADICAL
AND
THE
COREDUCTIVE
RADICAL
.
406
THE
STRUCTURE
OF
REDUCTIVE
PRO-LIE
GROUPS
.
412
POSTSCRIPT
.
419
10
SPLITTING
THEOREMS
FOR
PRO-LIE
GROUPS
.
423
SPLITTING
REDUCTIVE
GROUPS
SEMIDIRECTLY
.
424
VECTOR
GROUP
SPLITTING
IN
NONCOMMUTATIVE
GROUPS
.
436
THE
STRUCTURE
OF
PRONILPOTENT
AND
PROSOLVABLE
GROUPS
.
442
CONJUGACY
THEOREMS
.
451
POSTSCRIPT
.
454
XX
CONTENTS
11
PROCOMPACT
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
AND
COMPACT
SUBGROUPS
OF
PRO-LIE
GROUPS
.
457
PROCOMPACT
MODULES
AND
LIE
ALGEBRAS
.
457
PROCOMPACT
LIE
ALGEBRAS
AND
COMPACTLY
EMBEDDED
LIE
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
464
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
OF
PRO-LIE
ALGEBRAS
.
469
CONJUGACY
OF
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
.
472
COMPACT
CONNECTED
GROUPS
.
483
COMPACT
SUBGROUPS
.485
POTENTIALLY
COMPACT
PRO-LIE
GROUPS
.
488
THE
CONJUGACY
OF
MAXIMAL
COMPACT
CONNECTED
SUBGROUPS
.
491
THE
ANALYTIC
SUBGROUPS
HAVING
A
FULL
LIE
ALGEBRA
.
500
MAXIMAL
COMPACT
SUBGROUPS
OF
CONNECTED
PRO-LIE
GROUPS
.
512
AN
ALTERNATIVE
OPEN
MAPPING
THEOREM
.
517
ON
THE
CENTER
OF
A
CONNECTED
PRO-LIE
GROUP
.
519
POSTSCRIPT
.
522
12
THE
STRUCTURE
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
527
THE
AUTOMORPHISM
GROUPS
OF
SEMISIMPLE
PRO-LIE
GROUPS
.
527
TOPOLOGICAL
GROUPS
WITH
PRO-LIE
IDENTITY
COMPONENT
.
534
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
538
MAXIMAL
COMPACT
SUBGROUPS
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
540
THE
CONJUGACY
OF
MAXIMAL
COMPACT
SUBGROUPS
IN
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
543
THE
STRUCTURE
OF
ALMOST
CONNECTED
PRO-LIE
GROUPS
.
544
POSTSCRIPT
.
544
13
ALMOST
CONNECTED
PRO-LIE
GROUPS
AND
THEIR
TOPOLOGY
.
547
ALMOST
CONNECTED
PRO-LIE
GROUPS
AND
THEIR
TOPOLOGY
.
547
POSTSCRIPT
.
556
14
IWASAWA
'
S
LOCAL
SPLITTING
THEOREM
.
557
LOCALLY
SPLITTING
LIE
GROUP
QUOTIENTS
OF
PRO-LIE
GROUPS
.557
THE
LIE
ALGEBRA
THEORY
OF
THE
LOCAL
SPLITTING
.
562
SPLITTING
ON
THE
GROUP
LEVEL
.
571
SOME
COMMENTS
ON
CONNECTEDNESS
.
576
POSTSCRIPT
.
577
15
CATALOG
OF
EXAMPLES
.
579
CLASSIFICATION
OF
THE
EXAMPLES
IN
THE
CATALOG
.
579
ABELIAN
PRO-LIE
GROUPS
.580
CONTENTS
XXI
A
SIMPLE
CONSTRUCTION
.
588
PRONILPOTENT
PRO-LIE
GROUPS
.
591
PROSOLVABLE
PRO-LIE
GROUPS
.
595
SEMISIMPLE
AND
REDUCTIVE
PRO-LIE
GROUPS
.
602
MIXED
GROUPS
.609
EXAMPLES
CONCERNING
THE
DEFINITION
OF
LIE
AND
PRO-LIE
GROUPS
.
611
ANALYTIC
SUBGROUPS
OF
PRO-LIE
GROUPS
.
615
EXAMPLES
CONCERNING
SIMPLE
CONNECTIVITY
.
616
EXAMPLE
CONCERNING
G-MODULE
THEORY
.
617
POSTSCRIPT
.
617
PANORAMIC
OVERVIEW
OF
THIS
BOOK
.
619
PART
1.
THE
BASE
THEORY
OF
PRO-LIE
GROUPS
.
625
PART
2.
THE
ALGEBRA
OF
PRO-LIE
ALGEBRAS
.
639
PART
3.
THE
FINE
LIE
THEORY
OF
PRO-LIE
GROUPS
.
648
PART
4.
GLOBAL
STRUCTURE
THEORY
OF
CONNECTED
PRO-LIE
GROUPS
.
656
PART
5.
THE
ROLE
OF
COMPACTNESS
ON
THE
PRO-LIE
ALGEBRA
LEVEL
.
667
PART
6.
THE
ROLE
OF
COMPACT
SUBGROUPS
OF
PRO-LIE
GROUPS
.
675
PART
7.
LOCAL
SPLITTING
ACCORDING
TO
IWASAWA
.
686
A1
LIMITS
OF
TOPOLOGICAL
GROUPS
.
689
LIMITS
.
690
THE
EXTERNAL
APPROACH
TO
PROJECTIVE
LIMITS
.
704
PROJECTIVE
LIMITS
AND
LOCAL
COMPACTNESS
.709
THE
FUNDAMENTAL
THEOREM
ON
PROJECTIVE
LIMITS
.
716
THE
INTERNAL
APPROACH
TO
PROJECTIVE
LIMITS
.
719
PROJECTIVE
LIMITS
AND
COMPLETENESS
.
722
THE
CLOSED
SUBGROUP
THEOREM
.
725
THE
ROLE
OF
LOCAL
COMPACTNESS
.
729
THE
ROLE
OF
CLOSED
FULL
SUBCATEGORIES
IN
COMPLETE
CATEGORIES
.
731
POSTSCRIPT
.
734
A2
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.737
CHARACTER
GROUPS
OF
TOPOLOGICAL
VECTOR
SPACES
.
737
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
745
DUALITY
AT
WORK
FOR
THE
STRUCTURE
THEORY
OF
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
751
TOPOLOGICAL
PROPERTIES
OF
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
.
.
755
SUMMABILITY
IN
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.
758
CONTINUOUS
SYMPLECTIC
MAPS
ON
WEAKLY
COMPLETE
TOPOLOGICAL
VECTOR
SPACES
.758
XXII
CONTENTS
TENSOR
PRODUCTS
.
761
WEAKLY
COMPLETE
UNITAL
ALGEBRAS
.
762
THE
EXPONENTIAL
FUNCTION
.
766
WEAKLY
COMPLETE
SYMMETRIC
HOPF
ALGEBRAS
.
768
THE
SIGNIFICANCE
OF
GROUPLIKE
ELEMENTS
.
770
THE
SIGNIFICANCE
OF
PRIMITIVE
ELEMENTS
.
774
POSTSCRIPT
.
782
A3
THE
CAMPBELL-HAUSDORFF
FORMALISM
.785
POSTSCRIPT
.789
A4
VARIOUS
PIECES
OF
INFORMATION
ON
SEMISIMPLE
LIE
ALGEBRAS
.
791
BRACKETS
IN
SEMISIMPLE
LIE
ALGEBRAS
.
791
BRACKETS
IN
COMPACT
LIE
ALGEBRAS
.
792
MAXIMAL
COMPACTLY
EMBEDDED
SUBALGEBRAS
.
794
POSTSCRIPT
.
795
REFERENCES
.797
INDEX
.
809 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- |
| author_GND | (DE-588)115780734 (DE-588)132019515 |
| author_facet | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- |
| author_role | aut aut |
| author_sort | Hofmann, Karl H. 1932- |
| author_variant | k h h kh khh s a m sa sam |
| building | Verbundindex |
| bvnumber | BV049579692 |
| ctrlnum | (OCoLC)1415292649 (DE-599)DNB1312932678 |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV049579692 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T23:31:57Z |
| indexdate | 2024-07-20T04:35:51Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 3985470480 9783985470488 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034924633 |
| oclc_num | 1415292649 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xxii, 818 Seiten 23.5 cm x 16.5 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | EMS Press |
| record_format | marc |
| series | EMS Tracts in mathematics |
| series2 | EMS Tracts in mathematics |
| spelling | Hofmann, Karl H. 1932- Verfasser (DE-588)115780734 aut The structure of pro-lie groups Karl H. Hofmann, Sidney A. Morris Second edition Berlin, Germany EMS Press [2023] xxii, 818 Seiten 23.5 cm x 16.5 cm txt rdacontent n rdamedia nc rdacarrier EMS Tracts in mathematics 36 Lie theory of connected and almost connected pro-Lie groups completenes exponential function local Iwasawa splitting open mapping theorems Levi–Malcev splitting pro-Lie algebras pro-Lie groups quotient groups structure theory of locally compact groups Morris, Sidney A. 1947- Verfasser (DE-588)132019515 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-548-3 Vorangegangen ist 978-3-03719-032-6 EMS Tracts in mathematics 36 (DE-604)BV022480257 36 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034924633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20231211 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- The structure of pro-lie groups EMS Tracts in mathematics |
| title | The structure of pro-lie groups |
| title_auth | The structure of pro-lie groups |
| title_exact_search | The structure of pro-lie groups |
| title_exact_search_txtP | The structure of pro-lie groups |
| title_full | The structure of pro-lie groups Karl H. Hofmann, Sidney A. Morris |
| title_fullStr | The structure of pro-lie groups Karl H. Hofmann, Sidney A. Morris |
| title_full_unstemmed | The structure of pro-lie groups Karl H. Hofmann, Sidney A. Morris |
| title_short | The structure of pro-lie groups |
| title_sort | the structure of pro lie groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034924633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022480257 |
| work_keys_str_mv | AT hofmannkarlh thestructureofproliegroups AT morrissidneya thestructureofproliegroups AT europeanmathematicalsocietypublishinghouseethzentrumsewa27 thestructureofproliegroups |