Skew Lattice Workshop at CAUL, Lisbon

WORKING SEMINARS ON NONCOMMUTATIVE LATTICES

by

João Pita Costa

University of Ljubljana, Slovenia

Abstract: Pascual Jordan was the first to study noncommutative lattices in 1949. Skew lattices have been the most successful variation of noncommutative lattices. Jonathan Leech studied a more general version of these algebras and was later interested in their Boolean version termed skew Boolean algebras. The left-handed version of that case includes the class of Boolean skew algebras earlier studied by W.D. Cornish. R.J. Bignall, following ideas of Keimal and Werner, observed a subclass of skew Boolean algebras constitutes a decidable discriminator variety. In collaboration with J. Leech, R. Veroff, R.J. Bignall and M. Spinks have studied general properties of these algebras and used them in the study of multiple valued logic. A special attention has been always devoted to skew lattices in rings, that constitute a large class of examples, where Karin Cvetko-Vah and JPC answered several open questions. Today the classical dualities as Stone’s and Priestley’s are a focus of research in this context, where several relevant results have been achieved.

#1 Skew Lattice Theory

4.10.2012, 15:00, FCUL - Room 6.2.44

Basic concepts. Rectangular structure. Order structure. Decomposition theorems. Coset structure decomposition.

#2 Varieties of Skew Lattices

8.10.2012, 14:30, IIIUL - Room B3-01

Distributivity and cancellation. Varieties of skew lattices. Skew lattices in rings.

#3 Skew Boolean Algebras

12.10.2012, 14:30, IIIUL - Room B3-01

Skew Boolean algebras. Congruences. Subdirectly irreducibles. Aspects of Stone’s duality for skew lattices.

This workshop has already started. The three sessions are meant to be self-contained and independent form each other so that they can be followed at any availability. The email contact is also valid after the ending of this workshop. Go to the workshop page here.

Location: Centro de Álgebra da Universidade de Lisboa

Instituto para a Investigação Interdisciplinar da Universidade de Lisboa

Av. Prof. Gama Pinto, 2

1649-003 Lisboa

Portugal