To a finite subgroup Γ of SL2(C), we associate a new family of quantum algebras which are related to symplectic reflection algebras for wreath products Sl o Γ via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reflection algebras for Γ and construct for them a PBW basis. When Γ is a cyclic group, we are able to give more informati...

We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.

We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.

We find the normal form of nilpotent elements in semisimple Lie algebras that generalizes Jordan slN, using theory cyclic elements.