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In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra. [ABSTRACT FROM AUTHOR]

Let G be a group. We define an associative algebra Pk(x;G) that is a partition algebra whose diagrams have oriented edges labeled by elements of G. For G finite, we show that Pk(x;G) is the centralizer algebra of an action of the wreath product G≀Sn on tensor powers of its permutation module. [Copyright &y& Elsevier]