English

Vector bundles on degenerations of elliptic curves and Yang-Baxter equations

Algebraic Geometry 2009-07-11 v2 Quantum Algebra

Abstract

In this paper we introduce the notion of a geometric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter equation using the approach of Polishchuk. We also calculate certain solutions of the classical, quantum and associative Yang-Baxter equations obtained from moduli spaces of (semi-)stable vector bundles on Weierstrass cubic curves.

Keywords

Cite

@article{arxiv.0708.1685,
  title  = {Vector bundles on degenerations of elliptic curves and Yang-Baxter equations},
  author = {Igor Burban and Bernd Kreussler},
  journal= {arXiv preprint arXiv:0708.1685},
  year   = {2009}
}

Comments

140 pages, extended version, some typos corrected