On representations of Clifford algebras of ternary cubic forms

Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa

On representations of Clifford algebras of ternary cubic forms

Rings and Algebras 2011-07-11 v1 Algebraic Geometry

Authors: Emre Coskun , Rajesh S. Kulkarni , Yusuf Mustopa

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.

Keywords

Clifford algebras ternary cubic forms Ulrich bundles cubic surfaces irreducible representations vector bundles

Cite

@article{arxiv.1107.1506,
  title  = {On representations of Clifford algebras of ternary cubic forms},
  author = {Emre Coskun and Rajesh S. Kulkarni and Yusuf Mustopa},
  journal= {arXiv preprint arXiv:1107.1506},
  year   = {2011}
}

Comments

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

On representations of Clifford algebras of ternary cubic forms

Abstract

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