Joao Pita Costa: Flat Coset Decomposition of a Skew Lattice

 
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.