Class Partition Algebras as Centralizer Algebras of Wreath Products |
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Authors: | A Joseph Kennedy |
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Institution: | 1. Institute of Mathematical Sciences, C.I.T. Campus, Taramani , Chennai, India kennedy_2001in@yahoo.co.in |
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Abstract: | In this article, we study an important subalgebra of the tensor product partition algebra P k (x)? P k (y), denoted by P k (x, y) and called “Class Partition Algebra.” We show that the algebra P k (n, m) is the centralizer algebra of the wreath product S m ? S n . Furthermore, the algebra P k (x, y) and the tensor product partition algebra P k (x)? P k (y) are subalgebras of the G-colored partition algebra P k (x;G) and G-vertex colored partition algebra P k (x, G) respectively, for every group G with |G|=y ≥ 2k. |
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Keywords: | Centralizer algebra Direct product Partition algebra Wreath product |
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