| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 220; 2012; 131 ppMSC: 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.
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Table of Contents
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Chapters
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Introduction
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1. Yang–Baxter Equations
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2. Massey Products and AYBE – a Single Curve
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3. Massey Products and AYBE – Families of Curves
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4. Explicit Calculations – Smooth Curves
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5. Explicit Calculations – Singular Curves
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6. Summary
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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.
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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
