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三角李拟双代数胚的扭关系 被引量：1

Twisting Relation on Triangular Lie Quasi-Bialgbroid
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摘要 李拟双代数胚是李双代数胚的推广,它与扭泊松结构有密切的关系.本文证明了扭关系在李拟双代数胚范围内是等价关系,并给出了恰当和三角李拟双代数胚的定义,研究了它和YangBaxter方程的关系. Lie-quasi bialgebroid is the generalization of Lie bialgebroid.In this paper,the twisting relation is proved to be an equivalent relation with respect to Lie-quasi bialgebroid.Lastly,the notion of triangular Lie-quasi bialgebroid is introduced,and the relationship between triangular Lie-quasi bialgebroid and YangBaxter equation is studied.
作者 尹彦彬 刘玲
机构地区 河南大学数学与信息科学学院 北京信息科技大学理学院
出处 《河南大学学报（自然科学版）》 CAS 北大核心 2010年第6期551-555,共5页 Journal of Henan University:Natural Science
基金 河南省教育厅自然科学基金资助项目(2010B110005) 校内科研基金自然科学重点项目(2009ZZZD001)
关键词 源双代数胚 李拟双代数胚 Courant代数胚 Courant大括号 proto-bialgebroid Lie-quasi bialgebroid Courant algebroid Courant bracket
分类号 O186.1 [理学—基础数学]
  • 相关文献

参考文献5

  • 1Roytenberg D. On the structure of graded symplectic supermanifolds and eourant algebroids[J]. Quantization, Poisson brackets and beyond, 2001,315:169- 185.
  • 2Bangoura M, Kosmann-Schwarach Y. The double of a Jacobian quasi-bialgbra[J]. Lett. Math. phys. , 1993(28) :13-29.
  • 3Kosmann-Schwarzbach. Y. Quasi,twisted,and all that... in Poisson geometry and Lie algebroid theory[J]. The breadth of symplectic and poisson geometry, 2005,232:363-389.
  • 4YIN Yanbin HE Longguang.Dirac structures on protobialgebroids[J].Science China Mathematics,2006,49(10):1341-1352. 被引量：2
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二级参考文献14

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共引文献1

同被引文献13

  • 1HartwigJ, Larsson D, Silvestrov S. Deformations of Lie algebras using (J -derivations[J].Journal of Algebra, 2006, 295: 314-361.
  • 2Makhlouf A, Silvestrov S. Hom-algebra structures[J].Journal of Generalized Lie Theory and Applications, 2008, 2 (2) : 51-64.
  • 3Chen y, Wang y, Zhang L. The construction of Hom-Lie bialgebras[J].Journal of Lie Theory, 2010, 20: 767-783.
  • 4Sheng Y. Representations of Hom-Lie algebras[J]. Algebras and Representation Theory, 2012, 15: 1081 -1098.
  • 5Sheng v . Chen D. Hom-Lie 2-algehras[J].Journal of Algebra, 2013, 376: 174-195.
  • 6Larsson D, Silvestrov S. Quasi-Horn-Lie algebras, central extensions and 2-cocycle-like identities[J].Journal of Algebra, 2005, 288: 321 - 344.
  • 7Makhlouf A, Silvestrov S. Notes on formal deformations of Hom-associative and Hom-Lie algcbras[J]. Forum Mathernati?cum, 2010, 22(4): 715-739.
  • 8Laurent-Gengoux C, TelesJ. Hom-Lie algebroids[J].Journal of Geometry and Physics, 2013, 68: 69-75.
  • 9Kosmann-Schwarzbach Y. Nijenhuis structures on courant algebroids[J]. Bulletin of the Brazilian Mathematical, 2011, 42 (4): 625-649.
  • 10Caseiro R, De Nicola A, Nunes da CostaJ M. OnJacobi quasiNijenhuis algebroids and courant-Jacobi algebroid mor?phisms[J].Journal of Geometry and Physics, 2010, 60(6-8) :951-961.

引证文献1

河南大学学报（自然科学版）
2010年 第6期

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