# Joao Pita Costa: Flat Coset Decomposition of a Skew Lattice

Date: 19. 10. 2012

Source: Algebra seminar

Source: Algebra seminar

Sreda, 24. oktobra 2012, ob 10. uri v Plemljevem seminarju, Jadranska 19/III, Ljubljana

The foundations of the study of the coset structure of skew lattices were settled in 1993 by J. Leech that referred to this as the global geometry of such algebras. This approach has been quite successful on the recent past, decomposing a skew lattice into D-classes and relating partitions that these induce on each other. Such a decomposition has permitted a deeper insight into the generalization of distributivity for such algebras. As skew lattices can be seen as double regular bands, Kimura's decomposition holds in this theory and so does an analogous decomposition of the coset structure of a skew lattice. In this talk we will discuss several aspects of this topic and present some of its combinatorial implications.