Algebra Seminar talk

Toby Kenney
Graphical Algebras - A new approach to Congruence Lattices

In 1970, H. Werner gave a characterisation of which sublattices of a partition lattice were actually the congruences of an algebra on the underlying set. In his classification, he gave a new operation on partition lattices, called graphical composition of relations. We consider the question of which lattices with a notion of graphical composition can be represented as congruence lattices, with graphical composition of relations as in Werner.