Cover of Igor Burban: Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations

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

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American Mathematical Society

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131

978-0-8218-9207-7

0-8218-9207-X

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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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