Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
| Autor: | Igor Burban, Raschid Abedin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Lie bialgebra Yang–Baxter equation Complex system Geodetic datum Statistical and Nonlinear Physics Context (language use) Algebraic geometry Affine Lie algebra Mathematics - Algebraic Geometry Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics::Quantum Algebra Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Trigonometry Algebraic Geometry (math.AG) Mathematical Physics Mathematics |
| Popis: | This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples. |
| Databáze: | OpenAIRE |
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