On structure of homogenenous Wick ideals in Wick $*$-algebras with braided coefficients

摘要

We study the structure of Wick homogenenous ideals of higher degrees inquadratic algebras allowing Wick ordering. We present a method how to constructa homogeneous Wick ideal $\mathcal{I}_{n+1}$ of degree $n+1$ out of ahomogeneous Wick ideal $\mathcal{I}_n$ of degree $n$ so that$\mathcal{I}_{n+1}\subset\mathcal{I}_n$. We show that in some particular casesour procedure allows one to get a description of the largest homogeneous Wickideals of higher degrees having generators of the largest quadratic Wick idealonly. Finally we study classes of $*$-representations of Wick version of CCRannihilating certain homogeneous Wick ideals of degree higher than $2$.