Varieties of PBZ*-lattices

Roberto Giuntini, Claudia Mureşan, Francesco Paoli

Published 2018-04-22Version 1

We investigate the structure theory of some subvarieties of the variety of \emph{PBZ*-lattices}. These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and Kleene algebras expanded by an extra unary operation. We explore the connections between (subvarieties of) PBZ*-lattices and some neighbouring classes of algebras, including Stone algebras, as well as the relationships with the theories of subtractive and binary discriminator varieties.