On $C^{\ast }$-algebras generated by some deformations of CAR relations

Abstract

We study the representation theory and enveloping $C^{\ast }$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^{\ast }$-algebras under consideration as algebras of continuous matrix-functions satisfying certain boundary conditions is given.

In V.4 we give the description of the enveloping $C^{\ast }$-algebra for Wick analogue of CAR with 2 generators, see Section 4