**Contemporary Mathematics**

Volume: 688;
2017;
277 pp;
Softcover

MSC: Primary 16; 17; 20;

**Print ISBN: 978-1-4704-2805-1
Product Code: CONM/688**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

**Electronic ISBN: 978-1-4704-4042-8
Product Code: CONM/688.E**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

# Groups, Rings, Group Rings, and Hopf Algebras

Share this page *Edited by *
*Jeffrey Bergen; Stefan Catoiu; William Chin*

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.

#### Readership

Graduate students and research mathematicians interested in group theory, ring theory, and Hopf algebras.

# Table of Contents

## Groups, Rings, Group Rings, and Hopf Algebras

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions 116
- Nagata-Higman and rings with involution 1530
- On left symmetric color algebras 2540
- On the automorphism group of rational group algebras of finite groups 3348
- Graded simple modules and loop modules 5368
- 1. Introduction 5368
- 2. Graded simple modules 5671
- 3. Loop modules 5974
- 4. The groupoids \frM(𝜋) and \frN(𝜋) 6681
- 5. Graded simple modules with finite-dimensional centralizers 7388
- 6. Graded simple modules with simple centralizers 7994
- 7. Finite-dimensional graded simple modules in characteristic zero 8398
- References 85100

- Symmetric groups and fixed points on modules: An application of group theory to topology 87102
- Free unit groups in group rings and division rings: My collaboration with Don Passman 93108
- Group rings and Jordan decomposition 103118
- On the Toeplitz-Jacobson algebra and direct finiteness 113128
- Frobenius divisibility for Hopf algebras 125140
- Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property 139154
- 1. Introduction 139154
- 2. Cocommutative algebras, smash products, and the PBW theorem 142157
- 3. Characterization via deformation theory 148163
- 4. The case of bialgebras and Hopf algebras 150165
- 5. Generalized nil-Coxeter algebras and grouplike algebras 153168
- 6. Deformations over cocommutative algebras with nilpotent maximal ideals 160175
- Acknowledgments 166181
- References 166181

- 𝑝-subgroups of units in ℤ𝔾 169184
- On the classification of finite-dimensional semisimple Hopf algebras 181196
- Zero divisors in group rings of wreath products of groups 219234
- The lattice of submodules of a multiplicity-free module 237252
- Star group identities on units of group algebras 249264
- A note on group algebras of locally compact groups 259274
- Elementary construction of Lusztig’s canonical basis 265280
- 1. Introduction 265280
- 2. Notation 266281
- 3. Braid group action and PBW bases 267282
- 4. Equality mod 𝑞 and piecewise linear bijections 269284
- 5. Triangularity of bar involution and the canonical basis 270285
- 6. Properties of the canonical basis 272287
- 7. Example: Crystal operators from piecewise linear bijections 275290
- Acknowledgements 276291
- References 276291

- Back Cover Back Cover1294