辫子系数Wick $*$ -代数中齐次Wick理想的结构
On structure of homogenenous Wick ideals in Wick $*$-algebras with braided coefficients
摘要：
研究了允许Wick序的二次代数中高次Wick齐性理想的结构。给出了一个从一个$n$次的齐次Wick理想$\mathcal{I}_n$构造一个$n+1$次的齐次Wick理想$\mathcal{I}_{n+1}$的方法，使得$\mathcal{I}_{n+1}\subset\mathcal{I}_n$ .我们表明，在某些特殊情况下，我们的程序允许得到一个描述的最大的齐次威克理想的更高程度的最大的二次威克理想的发电机。最后研究了CCR的Wick型的$*$ -表示类零化了某些次高于$2$的齐次Wick理想.
英文摘要：
We study the structure of Wick homogenenous ideals of higher degrees in quadratic algebras allowing Wick ordering. We present a method how to construct a homogeneous Wick ideal $\mathcal{I}_{n+1}$ of degree $n+1$ out of a homogeneous Wick ideal $\mathcal{I}_n$ of degree $n$ so that $\mathcal{I}_{n+1}\subset\mathcal{I}_n$. We show that in some particular cases our procedure allows one to get a description of the largest homogeneous Wick ideals of higher degrees having generators of the largest quadratic Wick ideal only. Finally we study classes of $*$-representations of Wick version of CCR annihilating certain homogeneous Wick ideals of degree higher than $2$.
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