摘要
Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, 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^×n in FR^n.
Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, 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^×n in FR^n.
基金
Supported by National Natural Science Foundation of China(Grant No.11301195)
a research foundation of Huaqiao University(Grant No.2014KJTD14)
