Geometrization of Trigonometric Solutions of the Associative and Classical Yang–Baxter Equations

Author:

Polishchuk Alexander123

Affiliation:

1. Department of Mathematics, University of Oregon, Eugene, OR 97403, USA

2. National Research University Higher School of Economics, Moscow 101000, Russia

3. Korea Institute for Advanced Study, Seoul 02455, South Korea

Abstract

Abstract We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang–Baxter equations. In the associative case, the solutions come from symmetric spherical orders over the irreducible nodal curve of arithmetic genus $1$, while in the Lie case they come from spherical sheaves of Lie algebras over the same curve.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference16 articles.

1. Infinitesimal Hopf Algebras;Aguiar,2000

2. Solutions of the classical Yang–Baxter equation for simple Lie algebras;Belavin;Funct. Anal. Appl.,1982

3. The classical Yang–Baxter equation for simple Lie algebras;Belavin;Funktsional. Anal. Prilozhen.,1983

4. Non-commutative nodal curves and derived tame algebras;Burban,2021

5. Torsion free sheaves on Weierstrass cubic curves and the classical Yang–Baxter equation;Burban;Comm. Math. Phys.,2018

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