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Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics

Author: Pramod M. Achar

Publisher: American Mathematical Society

Published: 2014-08-27

Total Pages: 296

ISBN-13: 0821898523

This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Representation Theories and Algebraic Geometry

Author: A. Broer

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 455

ISBN-13: 9401591318

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The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Algebraic and Topological Aspects of Representation Theory

Author: Mee Seong Im

Publisher: American Mathematical Society

Published: 2024-01-22

Total Pages: 240

ISBN-13: 1470470349

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This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Representations of finite dimensional algebras and related topics in Lie theory and geometry

Author: Vlastimil Dlab

Publisher:

Published: 2004

Total Pages:

ISBN-13: 9781470430740

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These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional "instructional" workshop preceding the conference, there were also workshops on "Commutative Algebra, Algebraic Geometry and Representation Theory", "Finite Dimensional Algebras, Algebraic Groups and Lie Theory", and "Quantum Groups and Hall Algebras". These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional asso.

Recent Advances in Noncommutative Algebra and Geometry

Author: K. A. Brown

Publisher: American Mathematical Society

Published: 2024-05-30

Total Pages: 288

ISBN-13: 1470472392

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This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20–24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory. In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.

Representation Theory of Algebraic Groups and Quantum Groups

Author: Akihiko Gyoja

Publisher:

Published: 2011-03-30

Total Pages: 364

ISBN-13: 9780817672188

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Quantum Groups and Noncommutative Spaces

Author: Matilde Marcolli

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 247

ISBN-13: 3834898317

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This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.

Arithmetic and Geometry Around Quantization

Author: ÃzgÃ1⁄4r Ceyhan

Publisher:

Published: 2010-04-17

Total Pages: 302

ISBN-13: 9780817648329

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Representation Theory of Algebraic Groups and Quantum Groups

Author: Toshiaki Shoji

Publisher: American Mathematical Society(RI)

Published: 2004

Total Pages: 514

ISBN-13:

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A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.

Arithmetic and Geometry Around Quantization

Author: Özgür Ceyhan

Publisher: Springer Science & Business Media

Published: 2010-01-12

Total Pages: 292

ISBN-13: 0817648313

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This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.