A Generalization of the Brauer Algebra
نویسنده
چکیده
We study two variations of the Brauer algebra Bn(x). The first is the algebra An(x), which generalizes the Brauer algebra by considering loops. The second is the algebra Ln(x), the An(x)-subalgebra generated by diagrams without horizontal arcs. An(x) and Ln(x) exhibit for x 6= 0 an hereditary-chain indexed by all integers. Following the ideas of Martin [10] in the context of the partition algebra, and Doran et al. [4] for the Brauer algebra, we study semisimplicity of An(x) using restriction and induction in An(x) and Ln(x). Our main result is that An(x) is semisimple if x 6∈ Z and that Ln(x) is semisimple if x 6= 0.
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