Algebraic geometry of the classical Yang-Baxter equation and its generalizations / von Raschid Abedin. Paderborn, 2022
Inhalt
- Introduction
- Some facts about sheaves of algebras
- Basic definitions and properties
- Local triviality of sheaves of algebras
- Lattices in current algebras and sheaves of algebras on projective curves
- Formal generalized r-matrices
- Basic definitions and properties
- Lie subalgebras of g((z)) complementary to g[[z]]
- Formal r-matrices
- Algebro-geometric properties of formal generalized r-matrices
- Geometrization of formal generalized r-matrices.
- Properties of geometric data associated to formal generalized r-matrices
- Global aspects of formal generalized r-matrices
- Analytic generalized r-matrices
- Twisted loop algebras
- Lie bialgebras
- Basic definitions and properties
- Manin triples
- Twisting Lie bialgebra structures
- Examples of Lie bialgebras
- The Belavin-Drinfeld trichotomy
- Elliptic r-matrices
- Acyclic weakly g-locally free sheaves of algebras on elliptic curves.
- Classification of elliptic r-matrices.
- Trigonometric r-matrices
- Rational r-matrices
- Bibliography