Groups, Rings, Group Rings, and Hopf Algebras.

Groups, Rings, Group Rings, and Hopf Algebras.

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,...

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Bibliographic Details
Main Author: Chin, William
Other Authors: Bergen, Jeffrey, Catoiu, Stefan
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 2017.
Series:Contemporary Mathematics.
Subjects:
Group algebras > Congresses.
Group rings > Congresses.
Hopf algebras > Congresses.
Group algebras
Group rings
Hopf algebras
Conference papers and proceedings
Online Access:Click for online access
Table of 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; References; On left symmetric color algebras; 1. Introduction; 2. Left symmetric color algebras and nondegenerate color symmetric 2-cocycles; 3. Lifting the derivations of into the derivations of * ; Acknowledgements; References.
  • On the automorphism group of rational group algebras of finite groups1. Introduction; 2. Preliminaries; 3. Group algebras of simple groups; 4. Non-simple groups; References; Graded simple modules and loop modules; 1. Introduction; 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; References; Symmetric groups and fixed points on modules: An application of group theory to topology.
  • 1. Introduction2. Theorem 2.1; 3. The norm map; References; Free unit groups in group rings and division rings: My collaboration with Don Passman; 1. Introduction; 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; References; Group rings and Jordan decomposition; 1. Introduction; 2. Matrix Rings; 3. Group Rings; 4. Future Work; References; On the Toeplitz-Jacobson algebra and direct finiteness; 1. Introduction; 2. The results; 3. The direct finiteness conjecture and other outstanding problems.
  • AcknowledgmentReferences; Frobenius divisibility for Hopf algebras; Introduction; 1. Symmetric Algebras; 2. Hopf Algebras; Acknowledgement; References; Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property; 1. Introduction; 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; Acknowledgments; References; -subgroups of units in ℤ
  • 1. Introduction2. Known results; 3. Frobenius Groups; 4. Crucial examples for simple linear groups; 5. Conjugacy in larger group rings; References; 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; References; Zero divisors in group rings of wreath products of groups; 1. Introduction.; 2. Preliminaries.; 3. The Proof of Theorem I.

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