Dual Lie bialgebra structures of Poisson types
Abstract
Let $A=F[x,y]$ be the polynomial algebra on two variables $x,y$ over an algebraically closed field $F$ of characteristic zero. Under the Poisson bracket, $A$ is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of $A^*$ induced from the multiplication of the associative commutative algebra $A$ coincides with the maximal good subspace of $A^*$ induced from the Poisson bracket of the Poisson Lie algebra $A$. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products, five classes of new infinite dimensional Lie algebras are obtained.
- Publication:
-
Science in China A: Mathematics
- Pub Date:
- June 2015
- DOI:
- 10.1007/s11425-015-4991-7
- arXiv:
- arXiv:1502.00049
- Bibcode:
- 2015ScChA..58.1151S
- Keywords:
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- Mathematics - Quantum Algebra;
- 17B62;
- 17B05;
- 17B06
- E-Print:
- accepted for publication in SCIENCE CHINA Mathematics