Physical Sciences and Mathematics Commons^™

The Rook-Brauer Algebra, Elise G. Delmas

Mathematics, Statistics, and Computer Science Honors Projects

We introduce an associative algebra RB_k(x) that has a basis of rook-Brauer diagrams. These diagrams correspond to partial matchings on 2k vertices. The rook-Brauer algebra contains the group algebra of the symmetric group, the Brauer algebra, and the rook monoid algebra as subalgebras. We show that the basis of RB_k(x) is generated by special diagrams s_i, t_i (1 <= i < k) and p_j (1 <= j <= k), where the s_i are the simple transpositions that generated the symmetric group S_k, the t_i are the "contraction maps" which generate the …