On Deformations of Commutation Relation Algebras

TL;DR

This paper explores deformations of commutation relation algebras using Wick's algebras with symmetric operators, establishing conditions for consistent quotient algebras with additional relations.

Contribution

It introduces a framework for constructing well-defined quotient algebras from Wick's algebras under symmetry and consistency conditions.

Findings

Derived consistency conditions for algebraic actions

Constructed quotient algebras with new relations

Ensured algebraic actions are constant on equivalence classes

Abstract

This paper is on $C$ - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence classes. All consistency conditions follow from the above assumption. In this way we obtain well defined quotient algebras with some additional relations.