4-dimensional Artin-Schelter regular quadratic ${\tilde{H}}_4$-algebras

Abstract

In this paper, quadratic algebras on which ${\tilde{H}}_4$, the Heisenberg group of order 64, acts as degree-preserving algebra automorphisms are studied. In particular, we show that if $\mathcal{A}$ is a four-dimensional Artin-Schelter regular quadratic ${\tilde{H}}_4$-algebra with the degree one part isomorphic to the Schrödinger representation of ${\tilde{H}}_4$, then $\mathcal{A}$ is (a twist of) a four-dimensional Sklyanin algebra or (a twist of) a quantum Clifford algebra of global dimension 4.

Artin-Schelter regularity should be changed to correct Hilbert series throughout the paper