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 byproducts, five classes of new infinite dimensional Lie algebras are obtained.
 Publication:

Science in China A: Mathematics
 Pub Date:
 June 2015
 DOI:
 10.1007/s1142501549917
 arXiv:
 arXiv:1502.00049
 Bibcode:
 2015ScChA..58.1151S
 Keywords:

 Mathematics  Quantum Algebra;
 17B62;
 17B05;
 17B06
 EPrint:
 accepted for publication in SCIENCE CHINA Mathematics