Categorical, homological and combinatorial methods in algebra : AMS sectional meeting in honor of S.K. Jain's 80th birthday : Categorical, homological and combinatorial methods in algebra, March 16-18, 2018, Ohio State University, Columbus, Ohio / Ashish K. Srivastava [and three others] editors.

Format:

Book

Author/Creator:

Srivastava, Ashish K., editor.

American Mathematical Society. Sectional meeting (2018 : Columbus, Ohio), author.

Contributor:

Jain, S. K. (Surender Kumar), 1938- honoree.

Srivastava, Ashish K., editor.

Leroy, Andre (Andre Gerard), 1955- editor.

Herzog, Ivo, 1961- editor.

Guil Asensio, Pedro A., 1964- editor.

Series:

Contemporary mathematics (American Mathematical Society) ; Volume 751.

Contemporary mathematics ; Volume 751

Language:

English

Subjects (All):

Jain, S. K. (Surender Kumar), 1938---Congresses.

Jain, S. K.

Combinatorial analysis--Congresses.

Combinatorial analysis.

Categories (Mathematics)--Congresses.

Categories (Mathematics).

Algebra, Homological--Congresses.

Algebra, Homological.

Physical Description:

1 online resource (370 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2020]

Language Note:

English

Summary:

This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16-18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.

Contents:

Cover

Title page

Contents

Preface

On the Morita equivalence class of a finitely presented algebra

Acknowledgement

References

Quillen-Suslin theory for classical groups: Revisited over graded rings

Introduction

1. Definitions and Notations

2. Local-Global Principle for classical groups

3. Local-Global Principle for commutator subgroup

4. Auxiliary Result for Transvection subgroup

Acknowledgments

Natural elements of center of generalized quantum groups

1. Introduction

2. Generalized quantum groups

3. Elements of \BYcnprtrZomchipi via finite dimensional representations

4. Appendix

The global dimension of the generalized Weyl algebras ⁻¹ [ , ][ ,

, ]

2. The global dimension of Witten's, Woronowic'z deformations and quantum algebras

3. Proof of Theorem 1.6

4. The global dimension of ⁻¹ [ , ](\s, ) with affine automorphism \s

Quasi-quantum groups obtained from the Tannaka-Krein reconstruction theorem

2. Preliminaries

3. Reconstruction theory for quasi-quantum groups

4. Application: The QT quasi-Hopf algebra structure of a quantum double

5. Application: biproduct quasi-Hopf algebras

Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory

1. Total acyclicity and other terminology

2. Gorenstein objects

3. An equivalence of triangulated categories

4. Gorenstein flat-cotorsion modules

5. The stable category of Gorenstein flat-cotorsion modules

Tor-pairs: Products and approximations

1. Tor-pairs, relative dimensions and relative Mittag-Leffler modules

2. Tor-pairs closed under products

3. Approximations by modules in _{ }

References.

Model structures and relative Gorenstein flat modules and chain complexes

1. Preliminaries

2. Relative Gorenstein flat modules and chain complexes

3. The ℬ-flat stable module category.

4. Model structures arising from relative Gorenstein flat modules

Appendix A. The double dual of a definable class of chain complexes

Acknowledgements

Strongly flat modules and right noetherian chain domains

2. Strongly flat modules

3. Maximal flat epimorphic right ring of quotients

4. Right noetherian right chain domains

Structure theory of graded regular graded self-injective rings and applications

2. Structure theory of graded regular graded self-injective rings

3. Applications to Leavitt path algebras

On the bijectivity of the antipode and serial quantum groups

1. General results

2. Applications

3. Questions

Acknowledgment

Categories with negation

2. Background

3. The structure theory of ground triples via congruences

4. The geometry of prime systems

5. Tensor products

6. The structure theory of systemic modules via congruences

7. Functors among semiring ground triples and systems

8. Appendix A: Interface between systems and tropical mathematics

9. Appendix B: The categorical underpinning

Quasi-Baer module hulls and their examples

2. Quasi-Baer Rings and Modules

3. Quasi-Baer Hulls, Examples, and Counterexamples

Strict Mittag-Leffler modules and purely generated classes

1. Purity

2. Strict Mittag-Leffler and atomic modules

3. Pure generation

4. Separation

5. Countable self-separation

6. Finite separation in purely generated classes.

7. When strict \cL-atomic modules are strict ⟨\cL⟩-atomic

Rings over which cyclic modules are almost self-injective

3. Almost self- injective cyclic modules

4. Structure theorem for -rings

On isoclasses of maximal subalgebras determined by automorphisms

3. Presentations of Maximal Subalgebras

4. Type Path Algebras

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9781470456085

1470456087

OCLC:

1191754647