Yakymiv R. Representations of commutation relations with orthogonality conditions and their generalizations

Representations of *-algebras, generated by commutation relations generalazing canonical commutation and anti-commutation quantum mechanics relations are studied in the dissertation. Namely, we consider algebras of canonical commutation and anti-commutation relations with orthogonality conditions, q-deformation of canonical commutation relations with two degrees of freedom and Wick analog of generalized quons algebra with two degrees of freedom. We obtain classification of irreducible representations of q-deformed CAR on two generators. It is proved that universal C*-algebras generated by operators of Fock representation of deformed relations are pairwise isomorphic for all q from [0,1). A tame class of CAR with orthogonality condition with degrees of freedom more than two is described up to the unitary equivalence. The notion of integrable representation of Wick analog of generalized quans algebra on two generators is defined. Clsssification of integrable representations is obtained.