Coset Structure Decomposition

The foundations of the study of the coset structure of skew lattices were settled in 1993 by Jonathan 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 different D-classes induce on each other. As skew lattices are non commutative lattices that can be seen as double regular bands of semigroups, Kimura's decomposition holds in this theory and so does a analogous decomposition its coset structure. In this talk we will discuss the topic and present some combinatorial implications of such study.