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

Resource Information

The instance An introduction to hopf algebras, Robert G. Underwood, (electronic book) represents a material embodiment of a distinct intellectual or artistic creation found in University of Liverpool. This resource is a combination of several types including: Instance, Electronic.

Image

http://covers.openlibrary.org/b/isbn/9780387727660-M.jpg?default=false

Label

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

Medium

electronic book

Statement of responsibility

Robert G. Underwood

Instantiates

• An introduction to hopf algebras

Publication

• New York, Springer, 2011

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

Record ID

b2584484

Specific material designation

remote

Type of computer file

PDF.