Algebra Seminar talk
2022-08-17 (Wed! 10:15!)
Representability of generalisations of relation algebras
In 1948, Jónsson and Tarski defined proper relation algebras and asked whether every relation algebra was isomorphic to a proper relation algebra. This led to much research on the representability of relation algebras.
In 2013, Galatos and Jipsen studied quasi relation algebras (qRAs). This variety of algebras includes all relation algebras and has the additional property that its equational theory is decidable.
In this talk we will introduce representable distributive quasi relation algebras. These are defined via a construction involving posets with certain symmetry requirements. The definition gives rise to many interesting questions around the representability of distributive qRAs.