Dual Lie bialgebra structures of Poisson types

被引：0
作者：
Guang’Ai Song
YuCai Su
机构：
[1] Shandong Institute of Business and Technology,College of Mathematics and Information Science
[2] Tongji University,Department of Mathematics
来源：
Science China Mathematics | 2015年 / 58卷
关键词：
Poisson algebra; Virasoro-like algebra; Lie bialgebra; dual Lie bialgebra; good subspace; 17B62; 17B05; 17B06;
D O I：
暂无
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学科分类号：
摘要：
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A} = \mathbb{F}[x,y]$\end{document} be the polynomial algebra on two variables x, y over an algebraically closed field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}$\end{document} of characteristic zero. Under the Poisson bracket, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document} is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}*$\end{document} induced from the multiplication of the associative commutative algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document} coincides with the maximal good subspace of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}*$\end{document} induced from the Poisson bracket of the Poisson Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}$\end{document}. 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.
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页码：1151 / 1162
页数：11
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