Congruence classes of varieties of algebras
13/09/2013 Sexta-feira, 13 de Setembro de 2013, 15:45-16:45, IIIUL - Sala B1-01
Pierre Gillibert (CAUL)
Instituto para a Investigação Interdisciplinar da Universidade de Lisboa
The congruence class of a variety of algebras is the class of all isomorphic copies of congruences lattices of algebras in the variety.
Most of this talk resolves around the following two questions:
Is it possible to characterize lattices in a given congruence class?
To which extent a variety of algebras is determines by its congruence class?
The first question seems very difficult. It is even difficult, for a given class, to prove that a will-to-be characterization is not valid.
However, there is an efficient tool that allows to distinguish congruence classes, based on poset-indexed diagrams of algebras. I shall illustrate it with several examples.