University of Sydney Algebra Seminar

James East (University of Western Sydney)

Friday 6th September, 12:05-12:55pm, Carslaw 373

Idempotent generators in partition monoids

Write \(T\) and \(S\) for the full transformation semigroup and the symmetric group on the finite set \(\lbrace 1,\ldots,n\rbrace\). In 1966, John Howie showed that the complement \(T\setminus S\), the so-called singular part of \(T\), is generated by its idempotents. Subsequent work by Howie and others calculated the number of minimal idempotent generating sets for \(T\setminus S\) and also the rank and idempotent rank of other ideals of \(T\). In this talk, I'll outline the corresponding results for the partition monoid and some of its submonoids, including the Brauer and Jones monoids. This is joint work with Bob Gray (University of East Anglia).