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Noncommutative Geometry and Representation Theory in Mathematical Physics
Edited by: Jürgen Fuchs, Karlstads Universitet, Sweden, Jouko Mickelsson, KTH, AlbaNova-SCFAB, Stockholm, Sweden, Grigori Rozenblioum and Alexander Stolin, Göteborgs Universitet, Sweden, and Anders Westerberg, Karlstads Universitet, Sweden
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Contemporary Mathematics
2005; 384 pp; softcover
Volume: 391
ISBN-10: 0-8218-3718-4
ISBN-13: 978-0-8218-3718-4
List Price: US$109
Member Price: US$87.20
Order Code: CONM/391
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Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test.

In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influential in physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities.

This volume contains the plenary talks from the international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics.

The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitable for graduate students and researchers interested in mathematical physics.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

  • N. Bazunova -- Construction of graded differential algebra with ternary differential
  • C. Blohmann -- Calculation of the universal Drinfeld twist for quantum su(2)
  • M. Cederwall -- Thoughts on membranes, matrices and non-commutativity
  • C. Chryssomalakos and E. Okon -- Stable quantum relativistic kinematics
  • A. Davydov -- Cohomology of crossed algebras
  • T. Ekedahl -- Kac-Moody algebras and the cde-triangle
  • L. D. Faddeev -- Discretized Virasoro algebra
  • G. Felder and A. Varchenko -- Multiplication formulae for the elliptic gamma function
  • G. Fiore -- New approach to Hermitian \(q\)-differential operators on \(\mathbb{R}^N_q\)
  • J. Fröhlich, J. Fuchs, I. Runkel, and C. Schweigert -- Picard groups in rational conformal field theory
  • A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin -- On a class of representations of quantum groups
  • M. Gorelik and V. Serganova -- Shapovalov forms for Poisson Lie superalgebras
  • T. J. Hodges and M. Yakimov -- Triangular Poisson structures on Lie groups and symplectic reduction
  • Y.-Z. Huang -- Vertex operator algebras, fusion rules and modular transformations
  • L. Kadison -- Depth two and the Galois coring
  • N. Kamiya -- Examples of Peirce decomposition of generalized Jordan triple system of second order--Balanced cases
  • I. Kantor and G. Shpiz -- Graded representations of graded Lie algebras and generalized representations of Jordan algebras
  • E. Karolinsky, A. Stolin, and V. Tarasov -- Dynamical Yang-Baxter equation and quantization of certain Poisson brackets
  • R. Kashaev and N. Reshetikhin -- Braiding for quantum \(gl_2\) at roots of unity
  • C. Korff -- Solving Baxter's TQ-equation via representation theory
  • P. P. Kulish -- Noncommutative geometry and quantum field theory
  • E. Langmann -- Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system
  • D. Larsson and S. D. Silvestrov -- Quasi-Lie algebras
  • O. A. Laudal -- Time-space and space-times
  • J. Lukierski and V. D. Lyakhovsky -- Two-parameter extension of the \(\kappa\)-Poincaré quantum deformation
  • V. E. Nazaikinskii, A. Y. Savin, B.-W. Schulze, and B. Y. Sternin -- The index problem on manifolds with edges
  • D. Proskurin, Y. Savchuk, and L. Turowska -- On \(C^*\)-algebras generated by some deformations of CAR relations
  • O. K. Sheinman -- Krichever-Novikov algebras and their representations
  • S. D. Sinel'shchikov and L. Vaksman -- Quantum groups and bounded symmetric domains
  • D. Sternheimer -- Quantization is deformation
  • K. Szlachányi -- Monoidal Morita equivalence
  • V. N. Tolstoy -- Fortieth anniversary of extremal projector method for Lie symmetries
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