REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Leonid Chekhov

ABSTRACT: (joint with Marta Mazzocco) We begin with the semiclassical (Poisson) algebra originated from the reflection equation R_{12}S_1R^{t_1}_{12}S_2=S_2R^{t_1}S_1R_{12}
(in the standard tensorial notation). The corresponding algebras -- both classical and quantum-- admit Poisson restrictions to the space of block-upper-triangular matrices. We find the automorphisms of these restricted algebras and show that they are described by the corresponding braid-group action. We construct the corresponding groupoid structure as
well as affine generalizations of these algebras. We pose the question of the possible relation between these algebras and cluster algebras.