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反李三系的不变双线性型 被引量：6

INVARIANT BILINEAR FORMS ON ANTI-LIE TRIPLE SYSTEMS
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摘要 本文考察了反李三系和它的标准嵌入李超代数的Killing型之间的关系,并且证明了反李三系的反对称不变双线性型可以被唯一地扩张到它的标准嵌入李超代数。作为扩张定理的一个应用,得到了二次李和反李三系的唯一分解定理。 The authors investigate the relationship between the Killing form of an anti-Lie triple system and that of its standard imbedding Lie superalgebra, and prove that an invariant anti-symmetric bilinear form on an anti-Lie triple system can be uniquely extended to its standard imbedding Lie superalgebra. As an application of the extension theorem, finally, the unique decomposition theorems for the quadratic Lie and anti-Lie triple systems are obtained.
作者 张知学 李华君 董磊
机构地区 河北大学数学系 保定师范专科学校数学系 河北农业大学理学院数学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2004年第4期429-436,共8页 Chinese Annals of Mathematics
关键词 ε-李三系 李超代数 双线性型 ε-Lie triple system, Lie superalgebra, Bilinear form
分类号 O152.5 [理学—基础数学]
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参考文献10

  • 1[1]Kac, V. G., Lie superalgebra [J], Adv. in Math., 26(1977), 8-96.
  • 2[2]Lister, W. G., A structure theory in Lie triple systems [J], Trans. Amer. Math. Soc.,72(1952), 217-242.
  • 3[3]Faulkner, J. R. & Ferrar, J. C., Simple anti-Jordan pairs [J], Comm. Algebra, 8(1980),993-1013.
  • 4[4]Meyberg, K., Lectures on Algebras and Triple Systems [M], Lecture Notes, Univ. of Virginia, Charlottesville, 1972.
  • 5[5]Zhang, Z. X., Shi, Y. Q. & Zhao, L. N., Invariant symmetric bilinear forms on Lie triple system [J], Comm. Algebra, 30:11(2002), 5563-5573.
  • 6[6]Kamiya, N., A construction of anti-Lie triple systems form a class of triple systems [J],Mem. Fac. Sci. Shimane Univ., 22:12(1988), 51-62.
  • 7[7]Medina, A. & Revoy, Ph., Algebres de Lie et produit scalaire invariant [J], Ann. Sci.Ec. Norm. Sup., 4:18(1985), 553-561.
  • 8[8]Benamor, H. & Benayadi, S., Double extension of quadratic Lie superalgebras [J],Comm. Algebra, 27:1(1999), 67-88.
  • 9[9]Zhu, F. H. & Zhu, L. S., The uniqueness of decomposition of quadratic Lie algebras[J], Comm. Algebra, 29:11(2001), 5145-5154.
  • 10[11]Hopkins,N.C.,Nilpotent ideals in Lie and anti-Lie triple systems[J],J.Algebra,178(1995),480-492.

同被引文献35

  • 1Jacobson N., Lie and Jordan triple systems [J], Amer. J. Math., 1948, 71:148-170.
  • 2Loos O., Symmetric Spaces [M], Vol. I, New York: W. A. Benjamin Inc., 1969.
  • 3Kamiya N. and Okubo S. On triple systems and Yang-Baxter equations [M]// Proceedings of the Seventh International Colloquium on Differential Equations (Plovdiv, 1996), Utrecht: VSP, 1997:189-196.
  • 4Casas J. M., Loday J. L. and Pirashvili T., Leibniz n-algebras [J], Forum Math., 2002, 14:189 207.
  • 5Lister W. G., A structure theory of Lie triple systems [J], Trans. Amer. Math. Soc., 1952, 72:217-242.
  • 6Hopkins N. C., Nilpotent ideals in Lie and anti-Lie triple systems [J], J. Algebra, 1995, 178:480-492.
  • 7Hodge T. L., Lie triple systems, restricted Lie triple systems and algebraic groups [J], J. Algebra, 2001, 244: 533-580.
  • 8Calderon Martin A. J. and Piulestan M. F., On locally finite split Lie triple systems [J], Comm. Alg., 2004, 32:2443- 2455.
  • 9Hodge T. L. and Parshall B. J., On the representation theory of Lie triple systems [J], Trans. Amer. Math. Soc., 2002, 354:4359-4391.
  • 10Shi Y. Q. and Meng D. J., On derivations and automorphism group of Lie triple systems [J], J. Nankai University, 2002, 35:32-37.

引证文献6

二级引证文献1

数学年刊（A辑）
2004年 第4期

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