Algebraic Foundations Of Non Commutative Differential Geometry And Quantum Groups

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Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.

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Genre : Science
Author : Ludwig Pittner
Publisher : Springer Science & Business Media
Release : 2009-01-29
File : 476 Pages
ISBN-13 : 9783540478010


Quantum Groups And Their Representations

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This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.

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Genre : Science
Author : Anatoli Klimyk
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 568 Pages
ISBN-13 : 9783642608964


An Introduction To Noncommutative Differential Geometry And Its Physical Applications

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A thoroughly revised introduction to non-commutative geometry.

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Genre : Mathematics
Author : J. Madore
Publisher : Cambridge University Press
Release : 1999-06-24
File : 381 Pages
ISBN-13 : 9780521659918


Quantum Groups

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With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

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Genre : Science
Author : Vladimir K. Dobrev
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2017-07-10
File : 450 Pages
ISBN-13 : 9783110427783


Classical And Quantum Nonlocality

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This book provides an up-to-date understanding of the progress and current problems of the interplay of nonlocality in the classical theories of gravitation and quantum theory. These problems lie on the border between general relativity and quantum physics, including quantum gravity.

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Genre : Science
Author : Peter G. Bergmann
Publisher : World Scientific
Release : 2000
File : 258 Pages
ISBN-13 : 9789810242961


Classical And Quantum Nonlocality Proceedings Of The 16th Course Of The International School Of Cosmology And Gravitation

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This book provides an up-to-date understanding of the progress and current problems of the interplay of nonlocality in the classical theories of gravitation and quantum theory. These problems lie on the border between general relativity and quantum physics, including quantum gravity.

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Genre : Science
Author : P G Bergmann
Publisher : World Scientific
Release : 2000-08-21
File : 258 Pages
ISBN-13 : 9789814493147


Recent Advances In Noncommutative Algebra And Geometry

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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.

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Genre : Mathematics
Author : K. A. Brown
Publisher : American Mathematical Society
Release : 2024-05-30
File : 288 Pages
ISBN-13 : 9781470472399


Mathematical Reviews

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Genre : Mathematics
Author :
Publisher :
Release : 2005-06
File : 1108 Pages
ISBN-13 : UOM:39015062317246


Noncommutative Geometry And Quantum Groups

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Genre : Harmonic analysis
Author : Piotr M. Hajac
Publisher :
Release : 2003
File : 356 Pages
ISBN-13 : UOM:39015058281570


Noncommutative Localization In Algebra And Topology

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Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

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Genre : Mathematics
Author : Andrew Ranicki
Publisher : Cambridge University Press
Release : 2006-02-09
File : 332 Pages
ISBN-13 : 052168160X