Groups, rings, group rings, and Hopf algebras : international conference in honor of Donald S. Passman's 75th birthday, October 2-4, 2015, Loyola University, Chicago, IL : AMS special session in honor of Donald S. Passman's 75th birthday, October 3-4, 2015, Loyola University, Chicago, IL / Jeffrey Bergen, Stefan Catoiu, William Chin, editors.

Format:

Book

Contributor:

Bergen, Jeffrey, 1955- editor.

Catoiu, Stefan, editor.

Chin, William, editor.

Passman, Donald S., 1940- honoree.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 688

Contemporary mathematics, 688 0271-4132

Language:

English

Subjects (All):

Group algebras--Congresses.

Group algebras.

Group rings--Congresses.

Group rings.

Hopf algebras--Congresses.

Hopf algebras.

Physical Description:

1 online resource (294 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

Summary:

This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2-4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3-4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.

Contents:

Cover

Title page

Contents

Preface

The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions

1. Introduction

2. The Dixmier-Moeglin equivalence under base change

3. Linear operators on rings

4. Proof of Theorem 1.6

Acknowledgments

References

Nagata-Higman and rings with involution

On left symmetric color algebras

2. Left symmetric color algebras and nondegenerate color symmetric 2-cocycles

3. Lifting the derivations of into the derivations of *

Acknowledgements

On the automorphism group of rational group algebras of finite groups

2. Preliminaries

3. Group algebras of simple groups

4. Non-simple groups

Graded simple modules and loop modules

2. Graded simple modules

3. Loop modules

4. The groupoids \frM( ) and \frN( )

5. Graded simple modules with finite-dimensional centralizers

6. Graded simple modules with simple centralizers

7. Finite-dimensional graded simple modules in characteristic zero

Symmetric groups and fixed points on modules: An application of group theory to topology

2. Theorem 2.1

3. The norm map

Free unit groups in group rings and division rings: My collaboration with Don Passman

2. Our first work

3. The following years

4. The proof of Theorem 3.2

5. Involutions in group rings

6. Our exploits in division rings

Group rings and Jordan decomposition

2. Matrix Rings

3. Group Rings

4. Future Work

On the Toeplitz-Jacobson algebra and direct finiteness

2. The results

3. The direct finiteness conjecture and other outstanding problems

Acknowledgment

References.

Frobenius divisibility for Hopf algebras

Introduction

1. Symmetric Algebras

2. Hopf Algebras

Acknowledgement

Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property

2. Cocommutative algebras, smash products, and the PBW theorem

3. Characterization via deformation theory

4. The case of bialgebras and Hopf algebras

5. Generalized nil-Coxeter algebras and grouplike algebras

6. Deformations over cocommutative algebras with nilpotent maximal ideals

-subgroups of units in ℤ

2. Known results

3. Frobenius Groups

4. Crucial examples for simple linear groups

5. Conjugacy in larger group rings

On the classification of finite-dimensional semisimple Hopf algebras

0. Introduction

1. Abelian extensions

2. Structure of ²_{ }(\myk _{ },\myk^{ },\tl)

3. The Isomorphism Theorems

4. Almost Abelian Hopf Algebras of Dimension \le ⁴

5. Some old classification results revisited

6. Appendices

Zero divisors in group rings of wreath products of groups

1. Introduction.

2. Preliminaries.

3. The Proof of Theorem I.

4. Proofs of Theorems II and III.

5. Embedding in simple Artinian rings and division rings.

6. Concluding remarks.

The lattice of submodules of a multiplicity-free module

2. Distributive Lattices.

3. Applications and Examples.

Star group identities on units of group algebras

2. Basic facts

3. SLC groups

4. Symmetric units

5. Star group identities

A note on group algebras of locally compact groups

1. Preliminaries

2. Automorphism-invariant group algebras of locally compact groups.

3. Generalized group algebras of locally compact groups

4. Open Problems

Elementary construction of Lusztig's canonical basis

2. Notation

3. Braid group action and PBW bases

4. Equality mod and piecewise linear bijections

5. Triangularity of bar involution and the canonical basis

6. Properties of the canonical basis

7. Example: Crystal operators from piecewise linear bijections

Back Cover.

Notes:

Includes bibliographical references at the end of each chapters.

Description based on print version record.