%0 Journal Article
%T On Tensor Spaces for Rook Monoid Algebras
%A Zhankui Xiao
%J Mathematics
%D 2014
%I arXiv
%X Let $m,n\in \mathbb{N}$, and $V$ be a $m$-dimensional vector space over a field $F$ of characteristic $0$. Let $U=F\oplus V$ and $R_n$ be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of $U^{\otimes n}$ in $FR_n$, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of $U^{\otimes n}$ in $FR_n$.
%U http://arxiv.org/abs/1411.6120v1