On representations of Clifford algebras of ternary cubic forms

Details On representations of Clifford algebras of ternary cubic forms On representations of Clifford algebras of ternary cubic forms

2011-07-07

arxiv.org/abs/1107.1506v1

Mathematics

Rings and Algebras

9 pages, to appear in proceedings for the conference "New Trends in Noncommutative Algebra: A Conference in Honor of Ken Goode

Scientific paper

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.

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