Natalia Popova (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

On the growth and *-representations of deformations of algebras associated with Coxeter graphs

We consider the class of algebras that are deformations of quotient algebras of group algebras of Coxeter groups. For algebras from this class the linear basis is found applying the "Diamond lemma". The dimensions of finite dimensional algebras are found and for infinite dimensional algebras we calculate the growth. For the finite-dimensional algebras we prove the spectral theorem. For the infinite-dimensional algebra, associated with Coxeter graph with three vertices and two edges of type 4, we describe new class of *-representations.

Joint work with Yu.S. Samoilenko and A.V. Strelets.