Kites and representations of pseudo MV-algebras

Abstract

We investigate the structure of perfect residuated lattices, focussing especially on perfect pseudo MV-algebras. We show that perfect pseudo MV-algebras can be represented as a generalised version of kites of Dvurečenskij and Kowalski, and that they are categorically equivalent to $\ell$-groups with a distinguished automorphism. We then characterise varieties generated by kites and describe the lattice of these varieties as a complete sublattice of the lattice of perfectly generated varieties of perfect pseudo MV-algebras.