Representations of relations with orthogonality condition and their deformations - Yakymiv, R. Y.; Proskurin, D. P.; Ostrovskyi, V. L. (Methods of Functional Analysis and Topology, 2012)
Irreducible representations of *-algebras A_q generated by relations of the form a_i^*a_i+a_ia_i^*=1, i=1,2, a_1^*a_2=qa_2a_1^*, where q(0,1) is fixed, are classified up to the unitary equivalence. The case q=0 is considered separately. It is shown that the C^*-algebras A_q^F and A_0^F generated by operators of Fock representations of A_q and A_0 are isomorphic for any q(0,1). A realisation of the universal C^*-algebra A_0 generated by A_0 as an algebra of continuous operator-valued functions is given.