Joao Pita Costa: On parallelogram laws for skew lattices

Abstract: Distributivity and cancellation in skew lattices are independent properties, unlike what happens in commutative lattices. In this talk we are going to present the relations between the varieties of strongly symmetric skew lattices, cacellative skew lattices and  symmetric skew lattices. We generalize the parallelogram laws stated earlier for cancellative skew lattices. These will characterize each one of the varieties.  Later we will present some combinatoric results that follow from the parallelogram laws.