Stability of C^*-algebra associated with the twisted CCR

TL;DR

This paper investigates the structure of a specific $C^*$-algebra linked to twisted CCR, demonstrating isomorphism across parameter values and faithfulness of the Fock representation.

Contribution

It proves the isomorphism of $C^*$-algebras for different parameters and establishes the faithfulness of the Fock representation on both algebraic and $C^*$-algebra levels.

Findings

$C^*$-algebras for different parameters are isomorphic

Fock representation is faithful on *-algebra and $C^*$-algebra levels

Results extend understanding of twisted CCR algebra structures

Abstract

The $C^*$-algebra associated with the twisted CCR constructed by W. Pusz and S.L. Woronowicz is considered. It is proved that the $C^*$-algebras corresponding to different values of parameter $0<=\mu<1$ are isomorphic. It is proved that Fock representation is faithful on both *-algebra and $C^*$-algebra levels.