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

**Abstract:**

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*.