A Quantum Groups Primer
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A Quantum Groups Primer
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Author : Shahn Majid
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-04
A Quantum Groups Primer written by Shahn Majid 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 2002-04-04 with Mathematics categories.
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians but will also be useful for mathematical physicists.
Hopf Algebras Quantum Groups And Yang Baxter Equations
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Author : Florin Felix Nichita
language : en
Publisher: MDPI
Release Date : 2019-01-31
Hopf Algebras Quantum Groups And Yang Baxter Equations written by Florin Felix Nichita and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-31 with Mathematics categories.
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
Quantum Riemannian Geometry
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Author : Edwin J. Beggs
language : en
Publisher: Springer Nature
Release Date : 2020-01-31
Quantum Riemannian Geometry written by Edwin J. Beggs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-31 with Science categories.
This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute. This requires a reinvention of differential geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than to actual points. Such a theory is needed for the geometry of Hopf algebras or quantum groups, which provide key examples, as well as in physics to model quantum gravity effects in the form of quantum spacetime. The mathematical formalism can be applied to any algebra and includes graph geometry and a Lie theory of finite groups. Even the algebra of 2 x 2 matrices turns out to admit a rich moduli of quantum Riemannian geometries. The approach taken is a `bottom up’ one in which the different layers of geometry are built up in succession, starting from differential forms and proceeding up to the notion of a quantum `Levi-Civita’ bimodule connection, geometric Laplacians and, in some cases, Dirac operators. The book also covers elements of Connes’ approach to the subject coming from cyclic cohomology and spectral triples. Other topics include various other cohomology theories, holomorphic structures and noncommutative D-modules. A unique feature of the book is its constructive approach and its wealth of examples drawn from a large body of literature in mathematical physics, now put on a firm algebraic footing. Including exercises with solutions, it can be used as a textbook for advanced courses as well as a reference for researchers.
Moduli Spaces And Vector Bundles
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Author : Steve Bradlow
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Steve Bradlow 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 2009-05-21 with Mathematics categories.
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Algebraic Cycles And Motives Volume 1
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Author : Jan Nagel
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-03
Algebraic Cycles And Motives Volume 1 written by Jan Nagel 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 2007-05-03 with Mathematics categories.
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Surveys In Geometry And Number Theory
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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-18
Surveys In Geometry And Number Theory written by Nicholas Young 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 2007-01-18 with Mathematics categories.
A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.
Integral Closure Of Ideals Rings And Modules
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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12
Integral Closure Of Ideals Rings And Modules written by Craig Huneke 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 2006-10-12 with Mathematics categories.
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Fusion Systems In Algebra And Topology
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Author : Michael Aschbacher
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-25
Fusion Systems In Algebra And Topology written by Michael Aschbacher 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 2011-08-25 with Mathematics categories.
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
Synthetic Differential Geometry
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Synthetic Differential Geometry written by Anders Kock 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 2006-06-22 with Mathematics categories.
This book, first published in 2006, details how limit processes can be represented algebraically.
Moonshine The First Quarter Century And Beyond
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Author : James Lepowsky
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-03
Moonshine The First Quarter Century And Beyond written by James Lepowsky 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 2010-06-03 with Mathematics categories.
This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.