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首页> 外文期刊>Siberian Mathematical Journal >Enveloping Algebras and Ideals of the Niltriangular Subalgebra of the Chevalley Algebra
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Enveloping Algebras and Ideals of the Niltriangular Subalgebra of the Chevalley Algebra

机译：Enveloping Algebras and Ideals of the Niltriangular Subalgebra of the Chevalley Algebra

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Abstract A simple complex Lie algebra is characterized by a root system documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ Phi $end{document} and a Chevalley basis with the integer structure constants. The well-known arbitrariness of their choice for the niltriangular subalgebra documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ NPhi(C) $end{document} essentially affects the Lie-admissible algebra documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ R_{Phi} $end{document} (in the sense of Albert) over a field documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ K $end{document} such that documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ R_{Phi}^{(-)}simeq NPhi(K) $end{document}. We study the uniqueness of the (nonassociative) enveloping algebras documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ R_{Phi} $end{document} of classical types. The enumeration of ideals of the Lie algebras documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ NPhi(K) $end{document} and documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ R_{Phi} $end{document} for documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ K=GF(q) $end{document} leads to the solution of some combinatorial problem listed in ACM SIGSAM Bulletin in 2001. The calculations of multiple combinatorial sums with documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$ q $end{document}-binomial coefficient use the integral representation method of combinatorial sums (the coefficient method).

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