Introduction to bosets

Speaker: David Easdown, University of Sydney

Abstract: A biordered set (boset for short) is a set equipped with two intertwining reflexive and transitive relations which satisfy certain axioms. When these coincide the boset becomes -- surprise surprise -- a poset! (This pleasant terminology was coined by Patrick Jordan.) Bosets were invented by Nambooripad, who gave his own version of a general theory of fundamental regular semigroups (which specializes to the usual classical theory of fundamental inverse semigroups due to Munn). This talk is an introduction to abstract bosets and the free semigroup on a boset (which is a key ingredient in showing bosets characterize all skeletons of idempotents of semigroups). Very little is known about this intriguing object! Brett McElwee calculated the ranks of its free subgroups when the boset comes from a very special class.