The geometry of infinite-dimensional groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2009]
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
3. Folge ; 51 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Softcoverausgabe ist nicht innerhalb der Serie erschienen |
| Beschreibung: | xii, 304 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540772620 3540772626 |
Internformat
MARC
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| 100 | 1 | |a Khesin, Boris A. |d 1964- |e Verfasser |0 (DE-588)120262487 |4 aut | |
| 245 | 1 | 0 | |a The geometry of infinite-dimensional groups |c Boris Khesin ; Robert Wendt |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xii, 304 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |v 51 | |
| 500 | |a Softcoverausgabe ist nicht innerhalb der Serie erschienen | ||
| 650 | 4 | |a Algèbres de Lie de dimension infinie | |
| 650 | 4 | |a Groupes de Lie | |
| 650 | 4 | |a Infinite dimensional Lie algebras | |
| 650 | 4 | |a Lie groups | |
| 650 | 0 | 7 | |a Unendlichdimensionale Lie-Gruppe |0 (DE-588)4530098-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Unendlichdimensionale Lie-Gruppe |0 (DE-588)4530098-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wendt, Robert |d 1971- |e Verfasser |0 (DE-588)12294755X |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 978-3-540-85205-6 |w (DE-604)BV043177869 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-77263-7 |
| 830 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 3. Folge ; 51 |w (DE-604)BV000899194 |9 51 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016771097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016771097 | ||
Datensatz im Suchindex
| _version_ | 1804138075000930304 |
|---|---|
| adam_text | Contents
Preface
........................................................
VII
Introduction
................................................... 1
I Preliminaries
.............................................. 7
1
Lie Groups and Lie Algebras
.............................. 7
1.1
Lie Groups and an Infinite-Dimensional Setting
....... 7
1.2
The Lie Algebra of a Lie Group
..................... 9
1.3
The Exponential Map
.............................. 12
1.4
Abstract Lie Algebras
.............................. 15
2
Adjoint and Coadjoint Orbits
............................. 17
2.1
The Adjoint Representation
........................ 17
2.2
The Coadjoint Representation
...................... 19
3
Central Extensions
...................................... 21
3.1
Lie Algebra Central Extensions
..................... 22
3.2
Central Extensions of Lie Groups
.................... 24
4
The
Euler
Equations for Lie Groups
....................... 26
4.1
Poisson
Structures on Manifolds
..................... 26
4.2
Hamiltonian Equations on the Dual of a Lie Algebra
... 29
4.3
A Riemannian Approach to the
Euler
Equations
...... 30
4.4
Poisson
Pairs and Bi-Hamiltonian Structures
.......... 35
4.5
Integrable
Systems and the Liouville-Arnold Theorem
. 38
5
Symplectic Reduction
.................................... 40
5.1
Hamiltonian Group Actions
......................... 41
5.2
Symplectic Quotients
.............................. 42
6
Bibliographical Notes
.................................... 44
II Infinite-Dimensional Lie Groups: Their Geometry, Orbits,
and Dynamical Systems
................................... 47
1
Loop Groups and
Affine Lie
Algebras
...................... 47
1.1
The Central Extension of the Loop Lie algebra
........ 47
χ
Contents
1.2 Coadjoint Orbits
of
Affine
Lie Groups
................ 52
1.3
Construction of the Central Extension of the Loop
Group
........................................... 58
1.4
Bibliographical Notes
.............................. 65
Diffeomorphisms of the Circle and the Virasoro-Bott Group
.. 67
2.1
Central Extensions
................................ 67
2.2
Coadjoint Orbits of the Group of Circle Diffeomorphisms
70
2.3
The Virasoro Coadjoint Action and Hill s Operators
... 72
2.4
The Virasoro-Bott Group and the Korteweg-de
Vries
Equation
......................................... 80
2.5
The Bi-Hamiltonian Structure of the KdV Equation
... 82
2.6
Bibliographical Notes
.............................. 86
Groups of Diffeomorphisms
............................... 88
3.1
The Group of Volume-Preserving Diffeomorphisms
and Its Coadjoint Representation
.................... 88
3.2
The
Euler
Equation of an Ideal Incompressible Fluid
... 90
3.3
The Hamiltonian Structure and First Integrals
of the
Euler
Equations for an Incompressible Fluid
.... 91
3.4
Semidirect Products: The Group Setting for an Ideal
Magnetohydrodynamics and Compressible Fluids
...... 95
3.5
Symplectic Structure on the Space of Knots
and the Landau-Lifschitz Equation
.................. 99
3.6
Diffeomorphism Groups as Metric Spaces
.............105
3.7
Bibliographical Notes
..............................109
The Group of Pseudodifferential Symbols
...................
Ill
4.1
The Lie Algebra of Pseudodifferential Symbols
........
Ill
4.2
Outer Derivations and Central Extensions of V DS
.....113
4.3
The
Manin
Triple of Pseudodifferential Symbols
.......117
4.4
The Lie Group of a-Pseudodifferential Symbols
.......119
4.5
The Exponential Map for Pseudodifferential Symbols
.. 122
4.6
Poisson
Structures on the Group
of Q-Pseudodifferential Symbols
...............
^
.....124
4.7
Integrable
Hierarchies on the
Poisson
Lie Group
(?щт
■ 129
4.8
Bibliographical Notes
..............................132
Double Loop and Elliptic Lie Groups
......................134
5.1
Central Extensions of Double Loop Groups
and Their Lie Algebras
.............................134
5.2
Coadjoint Orbits
..................................136
5.3
Holomorphic Loop Groups and Monodromy
..........138
5.4
Digression: Definition of the Calogero-Moser Systems
.. 142
5.5
The Trigonometric Calogero-Moser System
and
Affine
Lie Algebras
............................146
5.6
The Elliptic Calogero-Moser System and Elliptic Lie
Algebras
.........................................149
5.7
Bibliographical Notes
..............................152
Contents
XI
III
Applications
of Groups: Topological
and Holomorphic Gauge Theories
..........................155
1
Holomorphic Bundles and Hitchin Systems
.................155
1.1
Basics on Holomorphic Bundles
.....................155
1.2
Hitchin Systems
...................................159
1.3
Bibliographical Notes
..............................162
2
Poisson
Structures on Moduli Spaces
.......................163
2.1
Moduli Spaces of Flat Connections on Riemann
Surfaces
..........................................163
2.2
Poincaré
Residue and the Cauchy-Stokes Formula
.....170
2.3
Moduli Spaces of Holomorphic Bundles
..............173
2.4
Bibliographical Notes
..............................179
3
Around the Chern-Simons Functional
......................180
3.1
A Reminder on the Lagrangian Formalism
............180
3.2
The Topological Chern-Simons Action Functional
.....184
3.3
The Holomorphic Chern-Simons Action Functional
.... 187
3.4
A Reminder on Linking Numbers
....................189
3.5
The Abelian Chern-Simons Path Integral and Linking
Numbers
.........................................192
3.6
Bibliographical Notes
..............................196
4
Polar Homology
.........................................197
4.1
Introduction to Polar Homology
.....................197
4.2
Polar Homology of
Projective
Varieties
...............202
4.3
Polar Intersections and Linkings
.....................206
4.4
Polar Homology for
Affine
Curves
...................209
4.5
Bibliographical Notes
..............................211
Appendices
....................................................213
A.I Root Systems
...........................................213
1.1
Finite Root Systems
...............................213
1.2 Semisimple
Complex Lie Algebras
...................215
1.3 Affine
and Elliptic Root Systems
....................216
1.4
Root Systems and Calogero-Moser Hamiltonians
......218
A.
2
Compact Lie Groups
.....................................221
2.1
The Structure of Compact Groups
...................221
2.2
A Cohomology Generator for a Simple Compact Group
224
A.3 Krichever-Novikov Algebras
..............................225
3.1
Holomorphic Vector Fields on C* and the Virasoro
Algebra
..........................................225
3.2
Definition of the Krichever-Novikov Algebras
and Almost Grading
...............................226
3.3
Central Extensions
................................228
3.4 Affine
Krichever-Novikov Algebras, Coadjoint Orbits,
and Holomorphic Bundles
..........................231
A.4
Kahler
Structures on the Virasoro and Loop Group Coadjoint
Orbits
.................................................234
XII Contents
4.1
The
Kahler
Geometry of the Homogeneous Space
Diff(51)/Ã1
.......................................234
4.2
The Action of Diff^1) and
Kahler
Geometry
on the Based Loop Spaces
..........................237
A.5 Diffeomorphism Groups and Optimal Mass Transport
........240
5.1
The Inviscid Burgers Equation as a Geodesic Equation
on the Diffeomorphism Group
.......................240
5.2
Metric on the Space of Densities and the Otto Calculus
244
5.3
The Hamiltonian Framework of the Riemannian
Submersion
.......................................247
A.6 Metrics and Diameters of the Group of Hamiltonian
Diffeomorphisms
........................................250
6.1
The Hofer Metric and Bi-invariant Pseudometrics
on the Group of Hamiltonian Diffeomorphisms
........250
6.2
The Infinite L2-Diameter of the Group of Hamiltonian
Diffeomorphisms
..................................252
A.
7
Semidirect Extensions of the Diffeomorphism
Group and Gas Dynamics
................................256
A.8 The Drinfeld-Sokolov Reduction
..........................260
8.1
The Drinfeld-Sokolov Construction
..................260
8.2
The Kupershmidt-Wilson Theorem and the Proofs
___263
A.9 The Lie Algebra
fllœ
.....................................267
9.1
The Lie Algebra gt^ and Its Subalgebras
.............267
9.2
The Central Extension of gt^
.......................268
9.3
ç-Difference
Operators and gi^
.....................269
АЛО
Torus Actions on the Moduli Space of Flat Connections
......272
10.1
Commuting Functions on the Moduli Space
...........272
10.2
The Case of SU(2)
.................................274
10.3
SL(n, C) and the Rational Ruijsenaars-Schneider
System
...........................................277
References
.....................................................281
Index
..........................................................301
|
| adam_txt |
Contents
Preface
.
VII
Introduction
. 1
I Preliminaries
. 7
1
Lie Groups and Lie Algebras
. 7
1.1
Lie Groups and an Infinite-Dimensional Setting
. 7
1.2
The Lie Algebra of a Lie Group
. 9
1.3
The Exponential Map
. 12
1.4
Abstract Lie Algebras
. 15
2
Adjoint and Coadjoint Orbits
. 17
2.1
The Adjoint Representation
. 17
2.2
The Coadjoint Representation
. 19
3
Central Extensions
. 21
3.1
Lie Algebra Central Extensions
. 22
3.2
Central Extensions of Lie Groups
. 24
4
The
Euler
Equations for Lie Groups
. 26
4.1
Poisson
Structures on Manifolds
. 26
4.2
Hamiltonian Equations on the Dual of a Lie Algebra
. 29
4.3
A Riemannian Approach to the
Euler
Equations
. 30
4.4
Poisson
Pairs and Bi-Hamiltonian Structures
. 35
4.5
Integrable
Systems and the Liouville-Arnold Theorem
. 38
5
Symplectic Reduction
. 40
5.1
Hamiltonian Group Actions
. 41
5.2
Symplectic Quotients
. 42
6
Bibliographical Notes
. 44
II Infinite-Dimensional Lie Groups: Their Geometry, Orbits,
and Dynamical Systems
. 47
1
Loop Groups and
Affine Lie
Algebras
. 47
1.1
The Central Extension of the Loop Lie algebra
. 47
χ
Contents
1.2 Coadjoint Orbits
of
Affine
Lie Groups
. 52
1.3
Construction of the Central Extension of the Loop
Group
. 58
1.4
Bibliographical Notes
. 65
Diffeomorphisms of the Circle and the Virasoro-Bott Group
. 67
2.1
Central Extensions
. 67
2.2
Coadjoint Orbits of the Group of Circle Diffeomorphisms
70
2.3
The Virasoro Coadjoint Action and Hill's Operators
. 72
2.4
The Virasoro-Bott Group and the Korteweg-de
Vries
Equation
. 80
2.5
The Bi-Hamiltonian Structure of the KdV Equation
. 82
2.6
Bibliographical Notes
. 86
Groups of Diffeomorphisms
. 88
3.1
The Group of Volume-Preserving Diffeomorphisms
and Its Coadjoint Representation
. 88
3.2
The
Euler
Equation of an Ideal Incompressible Fluid
. 90
3.3
The Hamiltonian Structure and First Integrals
of the
Euler
Equations for an Incompressible Fluid
. 91
3.4
Semidirect Products: The Group Setting for an Ideal
Magnetohydrodynamics and Compressible Fluids
. 95
3.5
Symplectic Structure on the Space of Knots
and the Landau-Lifschitz Equation
. 99
3.6
Diffeomorphism Groups as Metric Spaces
.105
3.7
Bibliographical Notes
.109
The Group of Pseudodifferential Symbols
.
Ill
4.1
The Lie Algebra of Pseudodifferential Symbols
.
Ill
4.2
Outer Derivations and Central Extensions of V'DS
.113
4.3
The
Manin
Triple of Pseudodifferential Symbols
.117
4.4
The Lie Group of a-Pseudodifferential Symbols
.119
4.5
The Exponential Map for Pseudodifferential Symbols
. 122
4.6
Poisson
Structures on the Group
of Q-Pseudodifferential Symbols
.
^
.124
4.7
Integrable
Hierarchies on the
Poisson
Lie Group
(?щт
■ 129
4.8
Bibliographical Notes
.132
Double Loop and Elliptic Lie Groups
.134
5.1
Central Extensions of Double Loop Groups
and Their Lie Algebras
.134
5.2
Coadjoint Orbits
.136
5.3
Holomorphic Loop Groups and Monodromy
.138
5.4
Digression: Definition of the Calogero-Moser Systems
. 142
5.5
The Trigonometric Calogero-Moser System
and
Affine
Lie Algebras
.146
5.6
The Elliptic Calogero-Moser System and Elliptic Lie
Algebras
.149
5.7
Bibliographical Notes
.152
Contents
XI
III
Applications
of Groups: Topological
and Holomorphic Gauge Theories
.155
1
Holomorphic Bundles and Hitchin Systems
.155
1.1
Basics on Holomorphic Bundles
.155
1.2
Hitchin Systems
.159
1.3
Bibliographical Notes
.162
2
Poisson
Structures on Moduli Spaces
.163
2.1
Moduli Spaces of Flat Connections on Riemann
Surfaces
.163
2.2
Poincaré
Residue and the Cauchy-Stokes Formula
.170
2.3
Moduli Spaces of Holomorphic Bundles
.173
2.4
Bibliographical Notes
.179
3
Around the Chern-Simons Functional
.180
3.1
A Reminder on the Lagrangian Formalism
.180
3.2
The Topological Chern-Simons Action Functional
.184
3.3
The Holomorphic Chern-Simons Action Functional
. 187
3.4
A Reminder on Linking Numbers
.189
3.5
The Abelian Chern-Simons Path Integral and Linking
Numbers
.192
3.6
Bibliographical Notes
.196
4
Polar Homology
.197
4.1
Introduction to Polar Homology
.197
4.2
Polar Homology of
Projective
Varieties
.202
4.3
Polar Intersections and Linkings
.206
4.4
Polar Homology for
Affine
Curves
.209
4.5
Bibliographical Notes
.211
Appendices
.213
A.I Root Systems
.213
1.1
Finite Root Systems
.213
1.2 Semisimple
Complex Lie Algebras
.215
1.3 Affine
and Elliptic Root Systems
.216
1.4
Root Systems and Calogero-Moser Hamiltonians
.218
A.
2
Compact Lie Groups
.221
2.1
The Structure of Compact Groups
.221
2.2
A Cohomology Generator for a Simple Compact Group
224
A.3 Krichever-Novikov Algebras
.225
3.1
Holomorphic Vector Fields on C* and the Virasoro
Algebra
.225
3.2
Definition of the Krichever-Novikov Algebras
and Almost Grading
.226
3.3
Central Extensions
.228
3.4 Affine
Krichever-Novikov Algebras, Coadjoint Orbits,
and Holomorphic Bundles
.231
A.4
Kahler
Structures on the Virasoro and Loop Group Coadjoint
Orbits
.234
XII Contents
4.1
The
Kahler
Geometry of the Homogeneous Space
Diff(51)/Ã1
.234
4.2
The Action of Diff^1) and
Kahler
Geometry
on the Based Loop Spaces
.237
A.5 Diffeomorphism Groups and Optimal Mass Transport
.240
5.1
The Inviscid Burgers Equation as a Geodesic Equation
on the Diffeomorphism Group
.240
5.2
Metric on the Space of Densities and the Otto Calculus
244
5.3
The Hamiltonian Framework of the Riemannian
Submersion
.247
A.6 Metrics and Diameters of the Group of Hamiltonian
Diffeomorphisms
.250
6.1
The Hofer Metric and Bi-invariant Pseudometrics
on the Group of Hamiltonian Diffeomorphisms
.250
6.2
The Infinite L2-Diameter of the Group of Hamiltonian
Diffeomorphisms
.252
A.
7
Semidirect Extensions of the Diffeomorphism
Group and Gas Dynamics
.256
A.8 The Drinfeld-Sokolov Reduction
.260
8.1
The Drinfeld-Sokolov Construction
.260
8.2
The Kupershmidt-Wilson Theorem and the Proofs
_263
A.9 The Lie Algebra
fllœ
.267
9.1
The Lie Algebra gt^ and Its Subalgebras
.267
9.2
The Central Extension of gt^
.268
9.3
ç-Difference
Operators and gi^
.269
АЛО
Torus Actions on the Moduli Space of Flat Connections
.272
10.1
Commuting Functions on the Moduli Space
.272
10.2
The Case of SU(2)
.274
10.3
SL(n, C) and the Rational Ruijsenaars-Schneider
System
.277
References
.281
Index
.301 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Khesin, Boris A. 1964- Wendt, Robert 1971- |
| author_GND | (DE-588)120262487 (DE-588)12294755X |
| author_facet | Khesin, Boris A. 1964- Wendt, Robert 1971- |
| author_role | aut aut |
| author_sort | Khesin, Boris A. 1964- |
| author_variant | b a k ba bak r w rw |
| building | Verbundindex |
| bvnumber | BV035103149 |
| callnumber-first | Q - Science |
| callnumber-label | QA387 |
| callnumber-raw | QA387 |
| callnumber-search | QA387 |
| callnumber-sort | QA 3387 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)231885830 (DE-599)DNB986422398 |
| dewey-full | 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 |
| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035103149 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:14:54Z |
| indexdate | 2024-07-09T21:22:17Z |
| institution | BVB |
| isbn | 9783540772620 3540772626 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016771097 |
| oclc_num | 231885830 |
| open_access_boolean | |
| owner | DE-20 DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-384 DE-83 DE-703 DE-11 DE-898 DE-BY-UBR DE-188 |
| owner_facet | DE-20 DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-384 DE-83 DE-703 DE-11 DE-898 DE-BY-UBR DE-188 |
| physical | xii, 304 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |
| spelling | Khesin, Boris A. 1964- Verfasser (DE-588)120262487 aut The geometry of infinite-dimensional groups Boris Khesin ; Robert Wendt Berlin ; Heidelberg Springer [2009] © 2009 xii, 304 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 51 Softcoverausgabe ist nicht innerhalb der Serie erschienen Algèbres de Lie de dimension infinie Groupes de Lie Infinite dimensional Lie algebras Lie groups Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd rswk-swf Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 s DE-604 Wendt, Robert 1971- Verfasser (DE-588)12294755X aut Erscheint auch als Druck-Ausgabe, Paperback 978-3-540-85205-6 (DE-604)BV043177869 Erscheint auch als Online-Ausgabe 978-3-540-77263-7 Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 51 (DE-604)BV000899194 51 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016771097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khesin, Boris A. 1964- Wendt, Robert 1971- The geometry of infinite-dimensional groups Ergebnisse der Mathematik und ihrer Grenzgebiete Algèbres de Lie de dimension infinie Groupes de Lie Infinite dimensional Lie algebras Lie groups Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd |
| subject_GND | (DE-588)4530098-7 |
| title | The geometry of infinite-dimensional groups |
| title_auth | The geometry of infinite-dimensional groups |
| title_exact_search | The geometry of infinite-dimensional groups |
| title_exact_search_txtP | The geometry of infinite-dimensional groups |
| title_full | The geometry of infinite-dimensional groups Boris Khesin ; Robert Wendt |
| title_fullStr | The geometry of infinite-dimensional groups Boris Khesin ; Robert Wendt |
| title_full_unstemmed | The geometry of infinite-dimensional groups Boris Khesin ; Robert Wendt |
| title_short | The geometry of infinite-dimensional groups |
| title_sort | the geometry of infinite dimensional groups |
| topic | Algèbres de Lie de dimension infinie Groupes de Lie Infinite dimensional Lie algebras Lie groups Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd |
| topic_facet | Algèbres de Lie de dimension infinie Groupes de Lie Infinite dimensional Lie algebras Lie groups Unendlichdimensionale Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016771097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT khesinborisa thegeometryofinfinitedimensionalgroups AT wendtrobert thegeometryofinfinitedimensionalgroups |