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Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations
Igor Burban, Universität Bonn, Germany, and Bernd Kreussler, Mary Immaculate College, Limerick, Ireland

Memoirs of the American Mathematical Society
2012; 131 pp; softcover
Volume: 220
ISBN-10: 0-8218-7292-3
ISBN-13: 978-0-8218-7292-5
List Price: US$71
Individual Members: US$42.60
Institutional Members: US$56.80
Order Code: MEMO/220/1035
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In this paper the authors introduce the notion of a geometric associative \(r\)-matrix attached to a genus one fibration with a section and irreducible fibres. It allows them to study degenerations of solutions of the classical Yang-Baxter equation using the approach of Polishchuk. They 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.

Table of Contents

  • Introduction
  • Yang-Baxter equations
  • Massey products and AYBE--a single curve
  • Massey products and AYBE--families of curves
  • Explicit calculations--smooth curves
  • Explicit calculations--singular curves
  • Summary
  • Bibliography
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