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arXiv · 1107.1506

On representations of Clifford algebras of ternary cubic forms

Emre Coskun·Rajesh S. Kulkarni·Yusuf Mustopa
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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.

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Emre Coskun, Rajesh S. Kulkarni, Yusuf Mustopa. 2011-07-07. On representations of Clifford algebras of ternary cubic forms. https://arxiv.org/abs/1107.1506

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