A note on generic Clifford algebras of binary cubic forms

Abstract

We study the representation theoretic results of the binary cubic generic Clifford algebra $\mathcal{C}$, which is an Artin-Schelter regular algebra of global dimension five. In particular, we show that $\mathcal{C}$ is a PI algebra of PI degree three and compute its point variety and discriminant ideals. As a consequence, we give a necessary and sufficient condition on a binary cubic form $f$ for the associated Clifford algebra ${\mathcal{C}}_f$ to be an Azumaya algebra.

to appear Algebr. Represent. Theory