University of Sydney Algebra Seminar

James East (University of Western Sydney)

Friday 9 Oct, 12-1pm, Place: Carslaw 375

Motzkin monoids

Brauer algebras and Temperley-Lieb algebras arise in statistical mechanics (Potts models), representation theory (Schur-Weyl duality) and many other settings. Partial versions of these algebras (partial (or rook) Brauer algebras and Motzkin algebras) have recently been studied by several authors, including Halverson, Martin and Mazorchuk. The above algebras are twisted semigroup algebras of associated diagram monoids. This talk will focus on the Motzkin monoids and partial Brauer monoids. In particular, we study various combinatorial problems such as idempotent generation in ideals and minimal generating sets - an important role is played by number sequences arising from lattice paths, e.g. Catalan and Motzkin numbers. This is joint work with Igor Dolinka (Novi Sad) and Robert Gray (East Anglia).