An introduction to Hopf algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIV, 273 S. graph. Darst. |
| ISBN: | 9780387727653 |
Internformat
MARC
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| 008 | 111007s2011 d||| |||| 00||| eng d | ||
| 015 | |a 11,O09 |2 dnb | ||
| 020 | |a 9780387727653 |c hbk |9 978-0-387-72765-3 | ||
| 024 | 3 | |a 9780387727660 | |
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| 035 | |a (DE-599)BVBBV039621118 | ||
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| 100 | 1 | |a Underwood, Robert G. |e Verfasser |0 (DE-588)1015211801 |4 aut | |
| 245 | 1 | 0 | |a An introduction to Hopf algebras |c Robert G. Underwood |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XIV, 273 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Hopf-Algebra |0 (DE-588)4160646-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hopf-Algebra |0 (DE-588)4160646-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-72766-0 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024471519 | ||
Datensatz im Suchindex
| _version_ | 1804148467837173760 |
|---|---|
| adam_text | Contents
1
The Spectrum of a Ring
.................................................... 1
1.1
Introduction to the Spectrum
........................................ 1
1.2
The Associated Map of Spectra
..................................... 3
1.3 Nilpotent
Elements
................................................... 8
1.4
Chapter Exercises
.................................................... 11
2
The Zariski Topology on the Spectrum
.................................. 13
2.1
Some Topology
....................................................... 13
2.2
Basis for a Topological Space
....................................... 17
2.3
Sheaves
............................................................... 23
2.4
Representable Functors
.............................................. 27
2.5
Chapter Exercises
.................................................... 32
3
Representable Group Functors
........................................... 35
3.1
Introduction to Representable Group Functors
..................... 35
3.2
Homomorphisms of ¿i-Group Schemes
............................. 41
3.3
Short Exact Sequences
............................................... 47
3.4
An Example
.......................................................... 51
3.5
Chapter Exercises
.................................................... 53
4 Hopf
Algebras
............................................................... 55
4.1
Introduction to
Hopf
Algebras
....................................... 55
4.2
Dedekind Domains
................................................... 65
4.3 Hopf
Modules
........................................................ 70
4.4 Hopf
Orders
.......................................................... 82
4.5
Chapter Exercises
.................................................... 93
5
Valuations and Larson Orders
............................................ 95
5.
1 Valuations
............................................................. 95
5.2
Group Valuations
..................................................... 100
5.3
LarsonOrders
........................................................ 104
5.4
Chapter Exercises
.................................................... 1
í
3
Xl
xii Contents
6 Formal Group Hopf Orders............................................... 115
6.1 Formal
Groups
........................................................ 115
6.2 Formal Group Hopf Orders.......................................... 121
6.3
Chapter Exercises....................................................
128
7 Hopf Orders in KCP........................................................ 129
7.1
Classification of
Hopf Orders in KCP............................... 129
7.2
Chapter Exercises....................................................
139
8 Hopf Orders in
КСрг
....................................................... 141
8.1
The Valuation Condition.............................................
141
8.2
Some Cohomology
................................................... 148
8.3 Greither Orders....................................................... 155
8.4 Hopf Orders in KC4, KC9........................................... 171
8.5
Chapter Exercises....................................................
179
9 Hopf Orders in
КСръ
....................................................... 181
9.1
Duality
Hopf Orders in
КСръ
....................................... 181
9.2 Circulant
Matrices
and Hopf Orders in
КСрз
...................... 185
9.3
Chapter Exercises
.................................................... 194
10 Hopf Orders
and Galois
Module
Theory
................................ 195
10.1
Some Galois Theory
................................................. 195
10.2
Ramification
.......................................................... 202
10.3
Galois Extensions of Rings
.......................................... 213
10.4
Hopf-Galois Extensions of a Local Ring
............................ 220
10.5
The Normal Basis Theorem
.......................................... 226
10.6
Chapter Exercises
.................................................... 230
11
The Class Group of
a
Hopf
Order
........................................ 233
11.1
The Class Group of a Number Field
................................. 233
11.2
The Class Group of
a
Hopf
Order
................................... 240
11.3
The Hopf-Swan Subgroup
........................................... 246
11.4
Chapter Exercises
.................................................... 259
12
Open Questions and Research Problems
................................. 261
12.1
The Spectrum of a Ring
.............................................. 261
12.2 Hopf
Algebras
........................................................ 261
12.3
Valuations and Larson Orders
....................................... 262
12.4 Hopf
Orders in KCp2
................................................ 262
12.5 Hopf
Orders in KCpi
................................................ 263
12.6 Hopf
Orders and Galois Module Theory
............................ 264
12.7
The Class Group of
a
Hopf
Order
................................... 265
Bibliography
...................................................................... 267
Index
............................................................................... 271
Robert G.
Underwood
An Introduction to
Hopf
Algebras
The study of
Hopf
alggebrms apens many fields in mathematics including topology, algebraic
geometry, algebraic number theory, Galois module theory, cohomology of groups, and
formal groups and ha$ wide-ranging connections to fields from theoretical physics
to computer science, This text is imique in making this engaging subject accessible
to advanced graduate
щэ.4
beginning ^rmdiaate students and focuses on applications
to
«l^ebrsìe
number tibeory and Galois module theory» providing a
transition
йот
modern
яіцеЬга
to
Hopf
algebras.
After providing an
introduction
to the spectrum of a ring and the Zariski topology, the
text treats presheaves, sheaves, and representable group functors. In this way the student
transitions smoothly from basic algebraic geometry to
Hopf
algebras. The importance of
Hopf
orders in underscored with applications to algebraic number theory, Gmlois module
theory and the theory of formal groups. By the end of the book, readers will be familiar
with established results in the field and ready to pose research questions of their own.
An exercise set is included in each of twelve chapters with questions ranging in difficulty.
Open problems and research questions are presented in the last chapter. Prerequisites
include an understanding of the material on groups, rings, and fields normally covered
in a basic course in modern algebra.
|
| any_adam_object | 1 |
| author | Underwood, Robert G. |
| author_GND | (DE-588)1015211801 |
| author_facet | Underwood, Robert G. |
| author_role | aut |
| author_sort | Underwood, Robert G. |
| author_variant | r g u rg rgu |
| building | Verbundindex |
| bvnumber | BV039621118 |
| classification_rvk | SK 260 SK 230 |
| classification_tum | MAT 160f MAT 130f |
| ctrlnum | (OCoLC)759802203 (DE-599)BVBBV039621118 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:07:36Z |
| institution | BVB |
| isbn | 9780387727653 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024471519 |
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| physical | XIV, 273 S. graph. Darst. |
| publishDate | 2011 |
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| spelling | Underwood, Robert G. Verfasser (DE-588)1015211801 aut An introduction to Hopf algebras Robert G. Underwood New York, NY [u.a.] Springer 2011 XIV, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-72766-0 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Underwood, Robert G. An introduction to Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4160646-2 |
| title | An introduction to Hopf algebras |
| title_auth | An introduction to Hopf algebras |
| title_exact_search | An introduction to Hopf algebras |
| title_full | An introduction to Hopf algebras Robert G. Underwood |
| title_fullStr | An introduction to Hopf algebras Robert G. Underwood |
| title_full_unstemmed | An introduction to Hopf algebras Robert G. Underwood |
| title_short | An introduction to Hopf algebras |
| title_sort | an introduction to hopf algebras |
| topic | Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Hopf-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024471519&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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