New r-Matrices for Lie Bialgebra Structures over Polynomials

被引:0
作者
Iulia Pop
Julia Yermolova-Magnusson
机构
[1] University of Gothenburg,Department of Mathematical Sciences
来源
Letters in Mathematical Physics | 2010年 / 93卷
关键词
Primary 17B37; 17B62; Secondary 17B81; -matrix; Lie bialgebra; classical double; Lagrangian subalgebra; classical Yang–Baxter equation; modified Yang–Baxter equation;
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学科分类号
摘要
For a finite dimensional simple complex Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{g}}$$\end{document} , Lie bialgebra structures on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{g}\left[\left[u \right]\right]}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{g}\left[u\right]}$$\end{document} were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce r-matrices which correspond to Lie bialgebra structures over polynomials.
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页码:141 / 156
页数:15
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