The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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University of Sydney Algebra Seminar

James East (University of Sydney)

Friday 11th November, 12.05-12.55pm, Carslaw 157

Cellular algebras and inverse semigroups

Cellular algebras were introduced by Graham and Lehrer in 1996 to provide a unified framework for understanding the representation theory of several important algebras; examples include Hecke algebras of types A and B, Brauer algebras, Temperley-Lieb algebras, partition algebras and many more. In this talk we will investigate the cellularity of another class of algebras -- the inverse semigroup algebras. The semigroup algebra of a finite inverse semigroup turns out to be cellular if (i) the group algebras of its maximal subgroups are cellular, and (ii) the anti-involutions on these maximal subgroup algebras are compatible in a certain sense. We will investigate several key examples including the symmetric inverse semigroup (also known as the rook monoid) and the dual symmetric inverse semigroup. If time permits we will conclude with a review of some recent work of Wilcox who has extended these ideas to study a wider class of semigroups.