Recent Advances In Noncommutative Algebra And Geometry
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Recent Advances In Noncommutative Algebra And Geometry
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Author : K. A. Brown
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-30
Recent Advances In Noncommutative Algebra And Geometry written by K. A. Brown and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-30 with Mathematics categories.
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
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Author : Ali Chamseddine
language : en
Publisher: Springer Nature
Release Date : 2020-01-13
Advances In Noncommutative Geometry written by Ali Chamseddine and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-13 with Mathematics categories.
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.
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics
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Author : Pramod M. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-27
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics written by Pramod M. Achar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
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.
Emerging Applications Of Algebraic Geometry
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Author : Mihai Putinar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Emerging Applications Of Algebraic Geometry written by Mihai Putinar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Methods Of Noncommutative Geometry For Group C Algebras
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Author : Do Ngoc Diep
language : en
Publisher: CRC Press
Release Date : 1999-12-06
Methods Of Noncommutative Geometry For Group C Algebras written by Do Ngoc Diep and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-06 with Mathematics categories.
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.
Quantum Groups And Noncommutative Spaces
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Author : Matilde Marcolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Quantum Groups And Noncommutative Spaces written by Matilde Marcolli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-02 with Mathematics categories.
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.
Noncommutative Algebraic Geometry
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Author : Gwyn Bellamy
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-20
Noncommutative Algebraic Geometry written by Gwyn Bellamy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Computational Noncommutative Algebra And Applications
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Author : Jim Byrnes
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-03
Computational Noncommutative Algebra And Applications written by Jim Byrnes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-03 with Mathematics categories.
The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. One of the most important applications of geometric algebras to geometry is to the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed in several chapters of this multi-authored textbook, which resulted from the ASI meeting. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail. With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the book have emerged as key tools. The list of authors includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometric transforms, and computational algorithms required for realizing the potential of these new application fields.
Representation Theory Mathematical Physics And Integrable Systems
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Author : Anton Alekseev
language : en
Publisher: Springer Nature
Release Date : 2022-02-05
Representation Theory Mathematical Physics And Integrable Systems written by Anton Alekseev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-05 with Mathematics categories.
Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
Elements Of Noncommutative Geometry
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Author : Jose M. Gracia-Bondia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Elements Of Noncommutative Geometry written by Jose M. Gracia-Bondia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.