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Frontiers of Mathematics in China 2018年第5期13卷 1179-1187页

作者： Yu-Feng YAO Hao CHANG Department of Mathematics Shanghai Maritime University Shanghai 201306 China School of Mathematics and Statistics Central China Normal University Wuhan 430079 China

Let g = W1 be the witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. algebra, 2002, 250： 473-484], we show that the variety ∮（g） is reducible, and not equidimensional. Irreducible components of ∮（g） and their dimensions are precisely given. As a consequence, the variety ∮（g） is not normal.

关键词： witt algebra irreducible component dimension commuting variety

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Borel Subalgebras of the witt algebra

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Acta Mathematica Sinica,English Series 2015年第8期31卷 1348-1358页

作者： Yu Feng YAO Hao CHANG Department of Mathematics Shanghai Maritime University Department of Mathematics East China Normal University

Let F be an algebraically closed field of characteristic p 〉 3, and g be the witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.

关键词： witt algebra Borel subalgebra nilpotent element nilpotent cone automorphism group

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Infinite-dimensional 3-Lie algebras and their ：onnections to Harish-Chandra modules

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Frontiers of Mathematics in China 2017年第3期12卷 515-530页

作者： Ruipu BAI Zhenheng LI Weidong WANG College of Mathematics and Information Science Hebei University Baoding 071002 China Department of Mathematical Sciences University of South Carolina Aiken Aiken SC 29801 USA

We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the witt algebras and contain the smallest full toroidal Lie algebras without center.

关键词： 3-Lie algebra Harish-Chandra module witt algebra intermediate series module toroidal Lie algebra inner derivation algebra

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Derivations and Automorphism Group of Original Deformative Schrodinger-Virasoro algebra

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algebra Colloquium 2015年第3期22卷 517-540页

作者： Qifen Jiang Song Wang Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics TongJi University Shanghai 200092 China College of Information Technology Shanghai Ocean University Shanghai 201306 China

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the witt algebra and its tensor d... 详细信息

关键词： derivation algebra automorphism group Lie algebra Wg(a b) Lie algebraW(a b) witt algebra

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ENDOMORPHISMS OF LIE algebra F[t]a/dt

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Journal of Systems Science & Complexity 2004年第1期17卷 143-146页

作者： DUHong KeyLaboratoryofMathematicsMechanization AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China

Let F be a field of characteristic zero. W_n = F[t_1^(+-1), t_2^(+-1), ...,t_n^(+-1)] (partial deriv)/((partial deriv)t_1) + ... + F[t_1^(+-1), t_2^(+-1), ..., t_n^(+-1)](partial deriv)/((partial deriv)t_n) is the witt algebra over F, W_n^+ = F[t_1, t_2 ..., t_n](partial deriv)/((partial deriv)t_1) + ... + F[t_1, t_2 ..., t_n] (partial deriv)/((partialderiv)t_n) is Lie subalgebra of W_n. It is well known both W_n and W_n^+ are simple infinitedimensional Lie algebra. In Zhao's paper, it was conjectured that End(W_n^+) - witt algebra = Aut(W_n^+) andit was proved that the validity of this conjecture implies the validity of the well-known Jacobianconjecture. In this short note, we check the conjecture above for n = 1. We show End(W_1^+) - witt algebra =Aut(W_1^+).

关键词： endomorphism automorphism witt algebra

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