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

2007/08/13 by Igor Burban, Burban, Igor, Bernd Kreußler +1
Mathematics · Physics and Astronomy · #14D06 #14H60 #14H70 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0708.1685

openalex publication_date 2007/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Associative Analog of Lie Bialgebras
• Vector Bundles Over an Elliptic Curve

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