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LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

Yıl 2015, Cilt: 3 Sayı: 2, 42 - 53, 01.10.2015

Bakayoko I. Bangoura M.

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.

Yıl 2015, Cilt: 3 Sayı: 2, 42 - 53, 01.10.2015

Bakayoko I. Bangoura M.

Öz

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Bakayoko I. Bu kişi benim

Bangoura M. Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

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. Ekim 2015;3(2):42-53.
Chicago I., Bakayoko, ve Bangoura M. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics 3, sy. 2 (Ekim 2015): 42-53.
EndNote I. B, M. B (01 Ekim 2015) LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp Journal of Mathematics 3 2 42–53.
IEEE B. I. ve B. M., “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”, Konuralp J. Math., c. 3, sy. 2, ss. 42–53, 2015.
ISNAD I., Bakayoko - M., Bangoura. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics 3/2 (Ekim 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 ve Bangoura M. “LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS”. Konuralp Journal of Mathematics, c. 3, sy. 2, 2015, ss. 42-53.
Vancouver I. B, M. B. LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS. Konuralp J. Math. 2015;3(2):42-53.
 Kapak Resmi İndir
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