scholarly journals Another approach to Hom-Lie bialgebras via Manin triples

2020 ◽  
Vol 48 (7) ◽  
pp. 3109-3132 ◽  
Author(s):  
Yi Tao ◽  
Chengming Bai ◽  
Li Guo
Keyword(s):  
Lie Bialgebras ◽  
Manin Triples

scholarly journals Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang–Baxter Equation

2021 ◽  
Author(s):  
Raschid Abedin ◽  
Igor Burban
Keyword(s):  
Algebraic Geometry ◽  
Lie Algebra ◽  
Baxter Equation ◽  
Lie Bialgebra ◽  
Lie Bialgebras ◽  
Infinite Dimensional ◽  
Geometric Context ◽  
Trigonometric Solution ◽  
Manin Triples ◽  
Geometric Study

AbstractThis 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.

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