On representations of Clifford algebras of ternary cubic forms

Abstract

In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$. We study general properties of Ulrich bundles, and using a recent classification of Casanellas and Hartshorne, deduce the existence of irreducible representations of $C_f$ of every possible dimension.

9 pages, to appear in proceedings for the conference "New Trends in Noncommutative Algebra: A Conference in Honor of Ken Goodearl's 65th Birthday"