Type: Seminar

Modified: Wed 21 Feb 2018 1645; Fri 18 May 2018 1614

Distribution: World

Expiry: 1 Jul 2018

CalTitle1: Algebra Seminar: Congruences on diagram monoids

Auth: kevinc@120.88.165.116 (kcou7211) in SMS-WASM

James East (Western Sydney University) Friday 25 May, 12-1pm, Place: Carslaw 375 Title: Congruences on diagram monoids. Abstract: A congruence on a semigroup is an equivalence relation that is compatible with the semigroup operation. Congruences play a role in semigroup theory akin to that of normal subgroups in group theory; they govern the formation of quotient semigroups, are kernels of semigroup homomorphisms, and so on. In a major 1952 paper, A.I. Mal’cev classified the congruences of a full transformation semigroup: i.e., a semigroup consisting of all self-maps of a fixed set. In the finite case, the lattice of all such congruences forms a chain. In the infinite case, the situation is far more complicated, but Mal’cev gives a succinct description nevertheless. This talk will report on some recent work on congruences on diagram monoids; these include the partition, Brauer and Temperley-Lieb monoids, for example. The finite case is joint work with James Mitchell, Nik Ruskuc and Michael Torpey (all at St Andrews), and the infinite is joint with Ruskuc.