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Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations

Igor Burban Universität Bonn, Bonn, Germany
Bernd Kreussler Mary Immaculate College, Limerick, Ireland
Available Formats:
Electronic ISBN: 978-0-8218-9207-7
Product Code: MEMO/220/1035.E
List Price: $71.00 MAA Member Price:$63.90
AMS Member Price: $42.60 Click above image for expanded view Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations Igor Burban Universität Bonn, Bonn, Germany Bernd Kreussler Mary Immaculate College, Limerick, Ireland Available Formats:  Electronic ISBN: 978-0-8218-9207-7 Product Code: MEMO/220/1035.E  List Price:$71.00 MAA Member Price: $63.90 AMS Member Price:$42.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2202012; 131 pp
MSC: Primary 14; 16;

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.

• Chapters
• Introduction
• 1. Yang–Baxter Equations
• 2. Massey Products and AYBE – a Single Curve
• 3. Massey Products and AYBE – Families of Curves
• 4. Explicit Calculations – Smooth Curves
• 5. Explicit Calculations – Singular Curves
• 6. Summary
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Volume: 2202012; 131 pp
MSC: Primary 14; 16;

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.

• Chapters
• Introduction
• 1. Yang–Baxter Equations
• 2. Massey Products and AYBE – a Single Curve
• 3. Massey Products and AYBE – Families of Curves
• 4. Explicit Calculations – Smooth Curves
• 5. Explicit Calculations – Singular Curves
• 6. Summary
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