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具有三角分解李代数的积分元和中心扩张 被引量：2

Integrals and Central Extensions of a Lie Algebra with a Triangular Decomposition
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摘要 本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系.对于给定的广义限制普遍包络代数,我们确定了它的积分元并且提供了一种计算dim H2(L,F)的方法. In this paper, we apply the concept of the generalized restricted Lie algebra to study the relation of the integral and central extensions of a Lie algebra with a triangular decomposition. We determine the left integral of a given generalized restricted universal enveloping algebra u(?)L(L), and give a method to compute dimH2(L,F).
作者 蒋志洪 濮燕敏
机构地区 同济大学应用数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2005年第4期747-762,共16页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10271088) 博士点专项基金(20040247024)
关键词 广义限制李代数 积分元 中心扩张 Generalized restricted Lie algebra Integral Central extension
分类号 O152.5 [理学—基础数学]
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参考文献13

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  • 2Farnsteiner R., Dual space derivations and H2(L, F) of modular Lie algebras, Canad. J. Math., 1987, 399:1078-1106.
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同被引文献16

  • 1Holmes R. R. and Zhang Chaowen, Some simple modules for the restricted Cartan-type Lie algebras [J], J. Pure Appl. Algebra, 2002(173):135 165.
  • 2Zhang Chaowen, On simple modules for the restricted Lie algebras of Cartan type [J], Comm. Algebra, 2002, 30:5393-5429.
  • 3Shu Bin, The generalized restricted representations of graded lie algebras of Cartan type [J], J. Algebra, 1997, 194:157 177.
  • 4Weisfeiler B. J. and Kac V. G., Exponentials in Lie algebras of characteristic p [J], Izu Akad. Nauk SSSR Ser. Mat., 1971, 35:762-788.
  • 5Shen Guangyu, Variations of the classical Lie algebra G2 in low characteristics [J], Nova Journal of Algebra and Geometry, 1993, 2(3):217-243.
  • 6Humphreys J. E., Introduction to Lie Algebras and Representation Theory [M], New York, Heidelberg, Berlin: Springer-Verlag, 1972.
  • 7Liu Dong, The associative forms of G and its variations [J], Journal of China East Normal University (Natural Sciences), 2000, 4:1-8.
  • 8Strade H. and Farnsteiner R., Modular Lie Algebras and Their Representations [M], New York: Dekker, 1988.
  • 9Strade H., Representations of the Witt algebra [J], J. Algebra, 1977(49):595 605.
  • 10Chang H., Uber Witt sche Lie-ringe [J], Abh. Math. Sere. Univ. Hamburg, 1941(14):151- 184.

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数学学报（中文版）
2005年 第4期

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