This volume contains papers presented at the BSF-Gelbart Institute workshop, "Quantum Deformations of Algebras and their Representations", held 29 December 1991 to 3 January 1992 at Bar-Ilan University and the Weizmann Institute in Israel. This highly successful meeting attracted over 100 participants, bringing together internationally recognized specialists. Topics covered at the workshop ranged over many aspects of representation theory, including the geometry of reductive group actions, enveloping algebras of Lie algebras, deformation of algebras, and construction of quantum groups and their representation theory. Applications include invariants of knots and three-manifolds, current algebras, and string theory. Books in the series are published by the Bar-Ilan University and distributed worldwide by the American Mathematical Society.

A publication of the Bar-Ilan University. Distributed worldwide by the AMS.

Readership

Research mathematicians.

Table of Contents

• H. H. Andersen -- Quantum groups, invariants of \(3\)-manifolds and semisimple tensor categories
• A. S. Dzhumadil'daev -- Quasi-Lie bialgebra structures of \(sl_2\), Witt and Virasoro algebras
• K. Erdmann and M. Schaps -- Deformation of tame blocks and related algebras
• M. Gerstenhaber, A. Giaquinto, and S. D. Schack -- Construction of quantum groups from Belavin-Drinfel'd infinitesimals
• E. Getzler -- Cartan homotopy formulas and the Gaussmanin connection in cyclic homology
• A. Joseph -- Faithfully flat embeddings for minimal primitive quotients of quantized enveloping algebras
• D. Kazhdan and M. Verbitsky -- Cohomology of restricted quantized universal enveloping algebras
• G. Lusztig -- Tight monomials in quantized enveloping algebras
• V. L. Popov -- Singularities of closures of orbits
• D. E. Radford -- Irreducible representations of \({\mathcal U}_q(g)\) arising from \(\mathrm{Mod}^{\bullet }_{ C^{1/2}}\)
• C. M. Ringel -- Hall algebras revisited