Sukretniy K. On *-representations of *-algebras, generated by deformations of commutating relations of quantum mechanics.

The study of representation theory of finitely-generated *-algebras attracts special attention due to numerous appliactions in mathematical physics, operator theory, non-commutative probability etc. The thesis devoted to classification of irreducible representations and enveloping C*-algebras of certain deformations of canonical commutation and anti-commutation relations and to description of complexity of category of representations of free product of C*-algebras and pairs of q-commuting isometries. The classification of irreducible *-representations of deformation of CAR, contained in the class of generalized quonic relations, is presented. The definition of integrable *-representation of many-parameter deformation of twisted CCR is given and irreducible integrable representations are classified up to unitary equivalence. The criterion of *-wildness of ree products of finite-dimensional C*-algebras is proved. The generalization of Coburn-Berger-Lebow model is constructed for pairs of q-commuting isometries.