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On tensor spaces for rook monoid algebras

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Abstract

Let m, n ∈ ℕ, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ⊕ V and R n be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U ⊗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 ⊗n in FR n .

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P. R. China

    Zhan Kui Xiao

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  1. Zhan Kui Xiao
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Correspondence to Zhan Kui Xiao.

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Supported by National Natural Science Foundation of China (Grant No. 11301195) and a research foundation of Huaqiao University (Grant No. 2014KJTD14)

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Xiao, Z.K. On tensor spaces for rook monoid algebras. Acta. Math. Sin.-English Ser. 32, 607–620 (2016). https://doi.org/10.1007/s10114-016-5546-8

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  • DOI: https://doi.org/10.1007/s10114-016-5546-8

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