Skew Lattices in CAUL 2012

Data de publicação: Jul 21, 2012 11:20:34 AM

Recently the postdoc project "A study of skew lattices: representations and completions" has been submitted to Fundação para a Ciência e Tecnologia to be supported as a post doctoral grant to João Pita Costa tutored by Maria João Gouveia and co-tutored by Karin Cvetko-Vah.

The project aims to explore aspects of the recent works on the generalizations of Stone and Priestley dualities for noncommutative skew lattices using the new available approaches. With this its intended a systematic study of the coset structure of distributive skew lattices and its impact on the generalization of dualities in this context. Moreover, we will work on the construction of concrete canonical extensions of certain classes of skew lattices using topological representations. Furthermore, we will study of the dualizable varieties of skew lattices in the sense of the theory of natural dualities. Contribution to the study of finitely generated varieties of skew lattices would also be of interest. Follows the abstract of such project.

ABSTRACT

Skew lattices are noncommutative generalizations of lattices and have been studied in the past 20 years. Topological representations of algebras revealed to be useful in many settings. One classical example of such a representation is Stone duality which was recently generalized for varieties of skew lattices, namely the variety of skew Boolean algebras with intersections. Priestley duality for distributive lattices motivated a recent topic of interest and involvement: to generalize Priestley duality and obtain a representation for skew distributive lattices. This project views the establishment of topological representations for another classes of skew lattices, preferably in the spirit of natural dualities and the use of these representations to obtain concrete constructions of canonical extensions of skew lattices. The study of skew lattices’ coset structure seems to be close related. We shall look at several open problems using this new machinery, and aim for a deeper knowledge on skew lattices.