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

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Date
2007-03-22MFO Scientific Program
Research in Pairs 2007Series
Oberwolfach Preprints;2007,04Author
Burban, Igor
Kreußler, Bernd
Metadata
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Abstract
In this paper we introduce the notion of a gemetric 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.