# Noncommutative Geometry and Representation Theory in Mathematical Physics

Share this page *Edited by *
*Jürgen Fuchs; Jouko Mickelsson; Grigori Rozenblioum; Alexander Stolin; Anders Westerberg*

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

## Noncommutative Geometry and Representation Theory in Mathematical Physics

- Contents v6 free
- Preface ix10 free
- List of Participants xi12 free
- Construction of graded differential algebra with ternary differential 116 free
- Calculation of the universal Drinfeld twist for quantum su(2) 1126
- Thoughts on membranes, matrices and non-commutativity 2136
- Stable quantum relativistic kinematics 3146
- Cohomology of crossed algebras 4156
- Kac-Moody algebras and the cde-triangle 4964
- Discretized Virasoro algebra 5974
- Multiplication formulae for the elliptic gamma function 6984
- New approach to Hermitian q-differential operators on RNq 7590
- Picard groups in rational conformal field theory 85100
- On a class of representations of quantum groups 101116
- Shapovalov forms for Poisson Lie superalgebras 111126
- Triangular Poisson structures on Lie groups and symplectic reduction 123138
- Vertex operator algebras, fusion rules and modular transformations 135150
- Depth two and the Galois coring 149164
- Examples of Peirce decomposition of generalized Jordan triple system of second order — Balanced cases 157172
- Graded representations of graded Lie algebras and generalized representations of Jordan algebras 167182
- Dynamical Yang-Baxter equation and quantization of certain Poisson brackets 175190
- Braiding for quantum gl2 at roots of unity 183198
- Solving Baxter's TQ-equation via representation theory 199214
- Noncommutative geometry and quantum field theory 213228
- Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system 223238
- Quasi-Lie algebras 241256
- Time-space and space-times 249264
- Two-parameter extensions of the k-Poincaré quantum deformation 281296
- The index problem on manifolds with edges 289304
- On C*-algebras generated by some deformations of CAR relations 297312
- Krichever-Novikov algebras and their representations 313328
- Quantum groups and bounded symmetric domains 323338
- Quantization is deformation 331346
- Monoidal Morita equivalence 353368
- Fortieth anniversary of extremal projector method for Lie symmetries 371386