对称群的扭群代数中的几个因子分解
Some factorizations in the twisted group algebra of symmetric groups
摘要：
在本文中，我们将给出一个类似的分解在\cite{4}，\cite{5}，其中作者Svrtan和Meljanac检查某些矩阵分解的Fock样表示的多参数quon代数上的自由结合代数的非交换多项式配备多参数偏导数。为了用扭代数计算代替这些矩阵分解（从右边给出），我们首先考虑对称群$S_{n}$在$n^2$交换变量$X_{a\,b}$中的多项式环$R_{n}$上的自然作用，并且还引入扭群代数（由$S_{n}$在$R_{n}$上的作用定义），我们用${\mathcal{A}(S_{n})}$表示。在这里，我们考虑从左边给出的一些因式分解，因为它们更适合于计算非交换多项式的自由代数中的常数（=被所有多参数偏导数湮没的元素）。
英文摘要：
In this paper we will give a similar factorization as in \cite{4}, \cite{5}, where the autors Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative algebra of noncommuting polynomials equiped with multiparametric partial derivatives. In order to replace these matrix factorizations (given from the right) by twisted algebra computation, we first consider the natural action of the symmetric group $S_{n}$ on the polynomial ring $R_{n}$ in $n^2$ commuting variables $X_{a\,b}$ and also introduce a twisted group algebra (defined by the action of $S_{n}$ on $R_{n}$) which we denote by ${\mathcal{A}(S_{n})}$. Here we consider some factorizations given from the left because they will be more suitable in calculating the constants (= the elements which are annihilated by all multiparametric partial derivatives) in the free algebra of noncommuting polynomials.
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