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（Co）Homology and Universal Central Extension of Hom-Leibniz Algebras 被引量：21

（Co）Homology and Universal Central Extension of Hom-Leibniz Algebras
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摘要 Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili. Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.
作者 Yong Sheng CHENG
机构地区 Institute of Contemporary Mathematics & College of Mathematics and Information Science Wu Wen- Tsun Key Laboratory of Mathematics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第5期813-830,共18页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China （Grant Nos. 10825101, 11047030） and Natural Science Foundation of He＇nan Provincial Education Department （Grant No. 2010Bl10003）
关键词 Hom-Leibniz algebra （co）homology theory central extension Hom-Leibniz algebra, （co）homology theory, central extension
分类号 O172 [理学—基础数学] O152.5 [理学—基础数学]
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参考文献18

  • 1Loday, J. L., Pirashvili, T.: Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann., 296, 139-158 (1993).
  • 2Hartwig, J., Larsson, D., Silvestrov, S.: Deformations of Lie algebras using a-derivation. J. Algebra, 295, 314 361 (2006).
  • 3Makhlouf, A., Silvestrov, S.: Notes on formal deformations of Horn-associative and Horn-Lie algebras. Forum Math., 22(4), 715 739 (2010).
  • 4Gao, Y.: The second Leibniz homology group for Kac-Moody Lie algebras. Bull. Lond. Math. Soc., 32, 25-33 (2000).
  • 5Gao, Y.: Leibniz homology of unitary Lie algebras. J. Pure Appl. Algebra, 140, 33 56 (1999).
  • 6Wang, Q., Tan, S.: Leibniz central extension on a Block Lie algebra. Algebra CoUoq., 14(4), 713-720 (2007).
  • 7Liu, D., Lin, L.: On the toroidal Leibniz algebras. Acta Mathematica Sinica, English Series, 24(2), 227-240 (2008).
  • 8Yau, D.: Horn-algebras as deformations and homology. J. Lie Theory, 19, 409-421 (2009).
  • 9Loday, J. L.: Dialgebras, Lecture Notes in Mathematics, Vol. 1763, Springer, 2001, 7-66.
  • 10Casas, J., Datuashvili, T.: Noncommutative Leibniz-Poission algebras. Comm. Algebra, 34, 2507-2530 (2006).

同被引文献29

  • 1Hartwig J T, Larsson D, Sliverstrov S D. Deforma- tion of Lie Algebras Using cz-derivations [J ]. J Al- gebra, 2005,295(2) :314 -361.
  • 2Makhlouf A, Silvestrov S D. Hom-algebra Structure[ J ]. J. Gen. Lie Theory Appl,2008,2 (2) : 51 - 64.
  • 3Nourou ISSA A. Some Characterizations of Hom- Leibniz algebras [ DB/OL ]. ( 2010 - 11 - 08 ). ht- tp ://arxiv. org/pdf/1011. 1731. pdf.
  • 4Sheng Yunhe. Representations of Hom-Lie Algebra [ J]. Algebras and Representation Theory, 2012, 15(6) :1081 - 1098.
  • 5HartwigJ, Larsson D, Silvestrov S. Deformations of Lie algebras using (J -derivations[J].Journal of Algebra, 2006, 295: 314-361.
  • 6Makhlouf A, Silvestrov S. Hom-algebra structures[J].Journal of Generalized Lie Theory and Applications, 2008, 2 (2) : 51-64.
  • 7Chen y, Wang y, Zhang L. The construction of Hom-Lie bialgebras[J].Journal of Lie Theory, 2010, 20: 767-783.
  • 8Sheng Y. Representations of Hom-Lie algebras[J]. Algebras and Representation Theory, 2012, 15: 1081 -1098.
  • 9Sheng v . Chen D. Hom-Lie 2-algehras[J].Journal of Algebra, 2013, 376: 174-195.
  • 10Larsson D, Silvestrov S. Quasi-Horn-Lie algebras, central extensions and 2-cocycle-like identities[J].Journal of Algebra, 2005, 288: 321 - 344.

引证文献21

二级引证文献9

Acta Mathematica Sinica,English Series
2011年 第5期

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