Minimal H₃ actions and simple quotients of a discrete 6-dimensional nilpotent group

Abstract

A simple C^*-algebra is introduced that is generated by a minimal effective action of the (discrete, nilpotent, non-abelian) Heisenberg group H₃ on the torus T² It appears as a simple quotient of the group C^*-algebra C^*(H_{6, 4}) of a 6-dimensional discrete nilpotent group H_{6, 4}, and also as a C^*-crossed product generated by an action of Z² on T² The rest of the infinite dimensional simple quotients of C^*(H_{6, 4}) are identified and displayed as C^*-crossed products generated by minimal effective actions, and also as matrix algebras over simple C^*-algebras from groups of lower dimension.