REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: In
this talk, I will discuss a certain minimal factorization of the
elements in a finite lattice L called the canonical join
representation.The canonical join representation of an element w is the
unique "lowest" subset of L whose join is equal to w (where "lowest"
will be made precise). When each element in L has a canonical join
representation, we define the canonical join complex to be the abstract
simplicial complex of subsets A such that the join of A is a canonical
join representation. I will characterize the class of finite lattices
whose canonical join complex is flag, and discuss several examples,
including the lattice of torsion classes over a finite dimensional
associative algebra.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu