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The Resource An introduction to hopf algebras, Robert G. Underwood, (electronic book)

An introduction to hopf algebras, Robert G. Underwood, (electronic book)

Label
An introduction to hopf algebras
Title
An introduction to hopf algebras
Statement of responsibility
Robert G. Underwood
Creator
Contributor
Subject
Language
eng
Summary
With wide-ranging connections to fields from theoretical physics to computer science, Hopf algebras offer students a glimpse at the applications of abstract mathematics. This book is unique in making this engaging subject accessible to advanced undergraduate and beginning graduate students. After providing a self-contained introduction to group and ring theory, the book thoroughly treats the concept of the spectrum of a ring and the Zariski topology. In this way the student transitions smoothly from basic abstract algebra to Hopf algebras. The importance of Hopf orders is underscored with appl
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Underwood, Robert G
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
http://library.link/vocab/subjectName
Hopf algebras
Label
An introduction to hopf algebras, Robert G. Underwood, (electronic book)
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 267-270) and index
Color
multicolored
Contents
  • An Introduction to Hopf Algebras -- Preface -- Contents -- Notation -- Chapter 1: The Spectrum of a Ring -- 1.1 Introduction to the Spectrum -- 1.2 The Associated Map of Spectra -- 1.3 Nilpotent Elements -- 1.4 Chapter Exercises -- Chapter 2: The Zariski Topology on the Spectrum -- 2.1 Some Topology -- 2.2 Basis for a Topological Space -- 2.3 Sheaves -- 2.4 Representable Functors -- 2.5 Chapter Exercises -- Chapter 3: Representable Group Functors -- 3.1 Introduction to Representable Group Functors -- 3.2 Homomorphisms of R-Group Schemes -- 3.3 Short Exact Sequences -- 3.4 An Example -- 3.5 Chapter Exercises
  • Chapter 4: Hopf Algebras -- 4.1 Introduction to Hopf Algebras -- 4.2 Dedekind Domains -- 4.3 Hopf Modules -- 4.4 Hopf Orders -- 4.5 Chapter Exercises -- Chapter 5: Valuations and Larson Orders -- 5.1 Valuations -- 5.2 Group Valuations -- 5.3 Larson Orders -- 5.4 Chapter Exercises -- Chapter 6: Formal Group Hopf Orders -- 6.1 Formal Groups -- 6.2 Formal Group Hopf Orders -- 6.3 Chapter Exercises -- Chapter 7: Hopf Orders in KCp -- 7.1 Classification of Hopf Orders in KCp -- 7.2 Chapter Exercises -- Chapter 8: Hopf Orders in KCp2 -- 8.1 The Valuation Condition -- 8.2 Some Cohomology -- 8.3 Greither Orders -- 8.4 Hopf Orders in KC4, KC9
  • 8.5 Chapter Exercises -- Chapter 9: Hopf Orders in KCp3 -- 9.1 Duality Hopf Orders in KCp3 -- 9.2 Circulant Matrices and Hopf Orders in KCp3 -- 9.3 Chapter Exercises -- Chapter 10: Hopf Orders and Galois Module Theory -- 10.1 Some Galois Theory -- 10.2 Ramification -- 10.3 Galois Extensions of Rings -- 10.4 Hopf-Galois Extensions of a Local Ring -- 10.5 The Normal Basis Theorem -- 10.6 Chapter Exercises -- Chapter 11: The Class Group of a Hopf Order -- 11.1 The Class Group of a Number Field -- 11.2 The Class Group of a Hopf Order -- 11.3 The Hopf-Swan Subgroup -- 11.4 Chapter Exercises
  • Chapter 12: Open Questions and Research Problems -- 12.1 The Spectrum of a Ring -- 12.2 Hopf Algebras -- 12.3 Valuations and Larson Orders -- 12.4 Hopf Orders in KCp2 -- 12.5 Hopf Orders in KCp3 -- 12.6 Hopf Orders and Galois Module Theory -- 12.7 The Class Group of a Hopf Order -- Bibliography -- Index
Control code
SPR755081046
Dimensions
unknown
Extent
xiv, 273 p.
Isbn
9780387727660
Specific material designation
remote
Type of computer file
PDF.
Label
An introduction to hopf algebras, Robert G. Underwood, (electronic book)
Publication
Bibliography note
Includes bibliographical references (p. 267-270) and index
Color
multicolored
Contents
  • An Introduction to Hopf Algebras -- Preface -- Contents -- Notation -- Chapter 1: The Spectrum of a Ring -- 1.1 Introduction to the Spectrum -- 1.2 The Associated Map of Spectra -- 1.3 Nilpotent Elements -- 1.4 Chapter Exercises -- Chapter 2: The Zariski Topology on the Spectrum -- 2.1 Some Topology -- 2.2 Basis for a Topological Space -- 2.3 Sheaves -- 2.4 Representable Functors -- 2.5 Chapter Exercises -- Chapter 3: Representable Group Functors -- 3.1 Introduction to Representable Group Functors -- 3.2 Homomorphisms of R-Group Schemes -- 3.3 Short Exact Sequences -- 3.4 An Example -- 3.5 Chapter Exercises
  • Chapter 4: Hopf Algebras -- 4.1 Introduction to Hopf Algebras -- 4.2 Dedekind Domains -- 4.3 Hopf Modules -- 4.4 Hopf Orders -- 4.5 Chapter Exercises -- Chapter 5: Valuations and Larson Orders -- 5.1 Valuations -- 5.2 Group Valuations -- 5.3 Larson Orders -- 5.4 Chapter Exercises -- Chapter 6: Formal Group Hopf Orders -- 6.1 Formal Groups -- 6.2 Formal Group Hopf Orders -- 6.3 Chapter Exercises -- Chapter 7: Hopf Orders in KCp -- 7.1 Classification of Hopf Orders in KCp -- 7.2 Chapter Exercises -- Chapter 8: Hopf Orders in KCp2 -- 8.1 The Valuation Condition -- 8.2 Some Cohomology -- 8.3 Greither Orders -- 8.4 Hopf Orders in KC4, KC9
  • 8.5 Chapter Exercises -- Chapter 9: Hopf Orders in KCp3 -- 9.1 Duality Hopf Orders in KCp3 -- 9.2 Circulant Matrices and Hopf Orders in KCp3 -- 9.3 Chapter Exercises -- Chapter 10: Hopf Orders and Galois Module Theory -- 10.1 Some Galois Theory -- 10.2 Ramification -- 10.3 Galois Extensions of Rings -- 10.4 Hopf-Galois Extensions of a Local Ring -- 10.5 The Normal Basis Theorem -- 10.6 Chapter Exercises -- Chapter 11: The Class Group of a Hopf Order -- 11.1 The Class Group of a Number Field -- 11.2 The Class Group of a Hopf Order -- 11.3 The Hopf-Swan Subgroup -- 11.4 Chapter Exercises
  • Chapter 12: Open Questions and Research Problems -- 12.1 The Spectrum of a Ring -- 12.2 Hopf Algebras -- 12.3 Valuations and Larson Orders -- 12.4 Hopf Orders in KCp2 -- 12.5 Hopf Orders in KCp3 -- 12.6 Hopf Orders and Galois Module Theory -- 12.7 The Class Group of a Hopf Order -- Bibliography -- Index
Control code
SPR755081046
Dimensions
unknown
Extent
xiv, 273 p.
Isbn
9780387727660
Specific material designation
remote
Type of computer file
PDF.

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