The Resource An introduction to hopf algebras, Robert G. Underwood, (electronic book)
An introduction to hopf algebras, Robert G. Underwood, (electronic book)
Resource Information
The item An introduction to hopf algebras, Robert G. Underwood, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item An introduction to hopf algebras, Robert G. Underwood, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- xiv, 273 p.
- 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
- Isbn
- 9780387727660
- Label
- An introduction to hopf algebras
- Title
- An introduction to hopf algebras
- Statement of responsibility
- Robert G. Underwood
- 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
- 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)
- 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)
- 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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