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Recent Advances in Noncommutative Algebra and Geometry

Recent Advances in Noncommutative Algebra and Geometry PDF Author: K. A. Brown
Publisher: American Mathematical Society
ISBN: 1470472392
Category : Mathematics
Languages : en
Pages : 288

Book Description
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.

Recent Advances in Noncommutative Algebra and Geometry

Recent Advances in Noncommutative Algebra and Geometry PDF Author: K. A. Brown
Publisher: American Mathematical Society
ISBN: 1470472392
Category : Mathematics
Languages : en
Pages : 288

Book Description
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.

Advances in Noncommutative Geometry

Advances in Noncommutative Geometry PDF Author: Ali Chamseddine
Publisher: Springer Nature
ISBN: 3030295974
Category : Mathematics
Languages : en
Pages : 753

Book Description
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Noncommutative Algebraic Geometry and Representations of Quantized Algebras

Noncommutative Algebraic Geometry and Representations of Quantized Algebras PDF Author: A. Rosenberg
Publisher: Springer Science & Business Media
ISBN: 9401584303
Category : Mathematics
Languages : en
Pages : 333

Book Description
This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.

Noncommutative Geometry

Noncommutative Geometry PDF Author: Alain Connes
Publisher: Springer Science & Business Media
ISBN: 9783540203575
Category : Mathematics
Languages : en
Pages : 372

Book Description
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Noncommutative Geometry, Arithmetic, and Related Topics

Noncommutative Geometry, Arithmetic, and Related Topics PDF Author: Caterina Consani
Publisher: JHU Press
ISBN: 1421403528
Category : Mathematics
Languages : en
Pages : 324

Book Description
Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.

Elements of Noncommutative Geometry

Elements of Noncommutative Geometry PDF Author: Jose M. Gracia-Bondia
Publisher: Springer Science & Business Media
ISBN: 1461200059
Category : Mathematics
Languages : en
Pages : 692

Book Description


Noncommutative Algebraic Geometry

Noncommutative Algebraic Geometry PDF Author: Gwyn Bellamy
Publisher: Cambridge University Press
ISBN: 1107129540
Category : Mathematics
Languages : en
Pages : 367

Book Description
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Methods of Noncommutative Geometry for Group C*-Algebras

Methods of Noncommutative Geometry for Group C*-Algebras PDF Author: Do Ngoc Diep
Publisher: CRC Press
ISBN: 9781584880196
Category : Mathematics
Languages : en
Pages : 4

Book Description
The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.

Noncommutative Structures in Mathematics and Physics

Noncommutative Structures in Mathematics and Physics PDF Author: Steven Duplij
Publisher: Springer Science & Business Media
ISBN: 9780792369998
Category : Science
Languages : en
Pages : 498

Book Description
A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

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

Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics PDF Author: Pramod M. Achar
Publisher: American Mathematical Society
ISBN: 0821898523
Category : Mathematics
Languages : en
Pages : 296

Book Description
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.