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LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

Year 2015, Volume: 3 Issue: 2, 42 - 53, 01.10.2015

Bakayoko I. Bangoura M.

Abstract

The aim of this paper is to introduce left-Hom-symmetric dial- gebras (which contain left-Hom-symmetric algebras or Hom-preLie algebras and Hom-dialgebras as special cases) and Hom-Poisson dialgebras. We give some examples and some construction theorems by using the composition con- struction. We prove that the commutator bracket of any left-Hom-symmetric dialgebra provides Hom-Leibniz algebra. We also prove that bimodules over Hom-dialgebras are closed under twisting. Next, we show that bimodules over Hom-dendriform algebras D extend to bimodules over the left-Hom-symmetric algebra associated to D. Finally, we give some examples of Hom-Poisson dial- gebras and prove that the commutator bracket of any Hom-dialgebra structure map leads to Hom-Poisson dialgebra.

Keywords

Hom-Leibniz algebras left-Hom-symmetric dialgebras left-Hom- symmetric algebras Hom-dendriform algebras

References

  • [1] A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. Vol.2 (2008), no. 2, 51-64.
  • [2] A. Makhlouf and D. Yau , Rota-Baxter Hom-Lie admissible algebras, Communication in Algebra, 23, no 3, 1231-1257, 2014.
  • [3] D. Yau, Non-commutative Hom-Poisson algebras, ArXiv : 1010.3408v1, 17 Oct 2010.
  • [4] D. Yau , Envelopping algebras of Hom-Lie algebras , J. Gen. Lie Theory Appl 2(2), 95-108, 2008.
  • [5] D. Yau, Module Hom-algebras, ArXiv:0812.4695v1, 26 Dec 2008.
  • [6] J. Hartwig, D. Larsson and S. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra 295 (2006), 314-361.
  • [7] J-L Loday, Dialgebras, arXiv : math/0102053v1, 7 Feb 2001.
  • [8] J. L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Ens. Math., 39 (1993), 269-293.
  • [9] M. Aguiar, In nitesimal bialgebras, pre-Lie and dendriform algebras, arXiv:math/0211074v3 [Math.QA] 16 Nov 2002.
  • [10] R. Felipe, A brief fondation of the left symmetric dialgebras, Comminicacion del CIMAT No I-11-02/18-03-2011 (MB/CIMAT).
  • [11] S. Benayadi and S. Hidri Quadratic Leibniz Algebras, Journal of Lie Theory, 24 (2014) 737-759.

Year 2015, Volume: 3 Issue: 2, 42 - 53, 01.10.2015

Bakayoko I. Bangoura M.

Abstract

References

  • [1] A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. Vol.2 (2008), no. 2, 51-64.
  • [2] A. Makhlouf and D. Yau , Rota-Baxter Hom-Lie admissible algebras, Communication in Algebra, 23, no 3, 1231-1257, 2014.
  • [3] D. Yau, Non-commutative Hom-Poisson algebras, ArXiv : 1010.3408v1, 17 Oct 2010.
  • [4] D. Yau , Envelopping algebras of Hom-Lie algebras , J. Gen. Lie Theory Appl 2(2), 95-108, 2008.
  • [5] D. Yau, Module Hom-algebras, ArXiv:0812.4695v1, 26 Dec 2008.
  • [6] J. Hartwig, D. Larsson and S. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra 295 (2006), 314-361.
  • [7] J-L Loday, Dialgebras, arXiv : math/0102053v1, 7 Feb 2001.
  • [8] J. L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Ens. Math., 39 (1993), 269-293.
  • [9] M. Aguiar, In nitesimal bialgebras, pre-Lie and dendriform algebras, arXiv:math/0211074v3 [Math.QA] 16 Nov 2002.
  • [10] R. Felipe, A brief fondation of the left symmetric dialgebras, Comminicacion del CIMAT No I-11-02/18-03-2011 (MB/CIMAT).
  • [11] S. Benayadi and S. Hidri Quadratic Leibniz Algebras, Journal of Lie Theory, 24 (2014) 737-759.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bakayoko I. This is me

Bangoura M. This is me

Publication Date October 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA I., B., & M., B. (2015). LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp Journal of Mathematics, 3(2), 42-53.
AMA I. B, M. B. LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp J. Math. October 2015;3(2):42-53.
Chicago I., Bakayoko, and Bangoura M. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 42-53.
EndNote I. B, M. B (October 1, 2015) LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp Journal of Mathematics 3 2 42–53.
IEEE B. I. and B. M., “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”, Konuralp J. Math., vol. 3, no. 2, pp. 42–53, 2015.
ISNAD I., Bakayoko - M., Bangoura. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics 3/2 (October 2015), 42-53.
JAMA I. B, M. B. LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp J. Math. 2015;3:42–53.
MLA I., Bakayoko and Bangoura M. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 42-53.
Vancouver I. B, M. B. LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp J. Math. 2015;3(2):42-53.
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