Cellularity of twisted semigroup algebras of regular semigroups

Speaker: Stewart Wilcox, University of Sydney

Abstract: We first discuss twisted semigroup algebras, in which the multiplication of two semigroup elements is a scalar times their usual product. The Temperley-Lieb and Brauer algebras are considered as examples. We then extend James's cellularity result, showing, under appropriate assumptions, that the twisted semigroup algebra of a regular semigroup is cellular if the twisted group algebras of the maximal subgroups are cellular. This is applied to the Brauer algebra.