Noncommutative structures in mathematics and physics : [proceedings of the NATO Advanced Research Workshop on Noncommutative Structures in Mathematics and Physics, Kiev, Ukraine, September 24-28, 2000

The concepts of noncommutative space-time and quantum groups have foundgrowing attention in quantum field theory and string theory. The mathematical concepts of quantum groups have been far developed by mathematicians and physicists of the Eastern European countries. Especially, V. G. Drinfeld fromUkraine, S. Woronowicz from Poland and L. D. Faddeev from Russia have beenpioneering the field. It seems to be natural to bring together these scientists with researchers in string theory and quantum field theory of the Western European countries. From another side, supersymmetry, as one of examples of noncommutative structure, was discovered in early 70's in the West by J. Wess (one of the co-Directors) and B. Zumino and in the East by physicists from UkraineV. P. Akulov and D. V. Volkov. Therefore, Ukraine seems to be a natural place to meet.

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

A presentation of achievements and ideas of Eastern and Western scientists, both mathematicians and physicists. The text includes presentations of work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, amongst others In gauge theories we consider differentiable manifolds as base manifolds and fibres that carry a representation of a Lie group.