BibTex RIS Cite

SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS

Year 2013, Volume: 14 Issue: 14, 1 - 9, 01.12.2013

A. Nourou Issa

Abstract

Some basic properties of Hom-Leibniz algebras are found. These
properties are the Hom-analogue of corresponding well-known properties of
Leibniz algebras. Considering the Hom-Akivis algebra associated to a given
Hom-Leibniz algebra, it is observed that the Hom-Akivis identity leads to an
additional property of Hom-Leibniz algebras, which in turn gives a necessary
and sufficient condition for Hom-Lie admissibility of Hom-Leibniz algebras. A
necessary and sufficient condition for Hom-power associativity of Hom-Leibniz
algebras is also found.

Keywords

Hom-Akivis algebra Hom-Leibniz algebra Hom-power associativity

References

  • M.A. Akivis, Local algebras of a multidimensional three-web, Siberian Math. J., 17 (1976), 3-8.
  • A.A. Albert, On the power-associativity of rings, Summa Brasil. Math., 2 (1948), 21-32.
  • H. Ataguema, A. Makhlouf, and S.D. Silvestrov, Generalization of n-ary Nambu algebras and beyond, J. Math. Phys., 50(8) (2009), 083501.
  • Sh.A. Ayupov and B.A. Omirov, On Leibniz algebras, in: Algebras and Op- erator Theory, Proceedings of the Colloquium in Tashkent, Kluwer (1998), 13.
  • D.W. Barnes, Engel subalgebras of Leibniz algebras, arXiv:0810.2849v1.
  • J.T. Hartwig, D. Larsson and S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra, 295 (2006), 314-361.
  • K.H. Hofmann and K. Strambach, Lie’s fundamental theorems for local ana- lytical loops, Pacific J. Math., 123 (1986), 301-327.
  • A.N. Issa, Hom-Akivis algebras, Comment. Math. Univ. Carolinae, 52(4) (2011), 485-500.
  • D. Larsson and S.D. Silvestrov, Quasi-Lie algebras, Contemp. Math., 391 (2005), 241-248.
  • J.-L. Loday, Une version non commutative des alg`ebres de Lie: les alg`ebres de Leibniz, Enseign. Math., 39 (1993), 269-293.
  • A. Makhlouf, Hom-alternative algebras and Hom-Jordan algebras, Int. Elec- tron. J. Algebra, 8 (2010), 177-190. A. Makhlouf, Paradigm of nonassociative Hom-algebras and Hom- superalgebras, Proceedings Jordan Structures in Algebra and Analysis Meet- ing, eds: J. Carmona Tapia, A. Morales Campoy, A. M. Peralta Pereira, M. I.
  • Ramirez Ivarez. Publishing House: Circulo Rojo (2010), 145-177.
  • A. Makhlouf and S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2008), 51-64.
  • D. Yau, Enveloping algebras of Hom-Lie algebras, J. Gen. Lie Theory Appl., 2 (2008), 95-108.
  • D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2009), 409-421.
  • D. Yau, Hom-Novikov algebras, J. Phys. A, 44 (2011), 085202.
  • D. Yau, Hom-Maltsev, Hom-alternative and Hom-Jordan algebras, Int. Elec- tron. J. Algebra, 11 (2012), 177-217.
  • D. Yau, Hom-power associative algebras, arXiv:1007.4118v1. A. Nourou Issa
  • D´epartement de Math´ematiques Universit´e d’Abomey-Calavi BP 4521 Cotonou 01, Benin e-mail: woraniss@yahoo.fr

Year 2013, Volume: 14 Issue: 14, 1 - 9, 01.12.2013

A. Nourou Issa

Abstract

References

  • M.A. Akivis, Local algebras of a multidimensional three-web, Siberian Math. J., 17 (1976), 3-8.
  • A.A. Albert, On the power-associativity of rings, Summa Brasil. Math., 2 (1948), 21-32.
  • H. Ataguema, A. Makhlouf, and S.D. Silvestrov, Generalization of n-ary Nambu algebras and beyond, J. Math. Phys., 50(8) (2009), 083501.
  • Sh.A. Ayupov and B.A. Omirov, On Leibniz algebras, in: Algebras and Op- erator Theory, Proceedings of the Colloquium in Tashkent, Kluwer (1998), 13.
  • D.W. Barnes, Engel subalgebras of Leibniz algebras, arXiv:0810.2849v1.
  • J.T. Hartwig, D. Larsson and S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra, 295 (2006), 314-361.
  • K.H. Hofmann and K. Strambach, Lie’s fundamental theorems for local ana- lytical loops, Pacific J. Math., 123 (1986), 301-327.
  • A.N. Issa, Hom-Akivis algebras, Comment. Math. Univ. Carolinae, 52(4) (2011), 485-500.
  • D. Larsson and S.D. Silvestrov, Quasi-Lie algebras, Contemp. Math., 391 (2005), 241-248.
  • J.-L. Loday, Une version non commutative des alg`ebres de Lie: les alg`ebres de Leibniz, Enseign. Math., 39 (1993), 269-293.
  • A. Makhlouf, Hom-alternative algebras and Hom-Jordan algebras, Int. Elec- tron. J. Algebra, 8 (2010), 177-190. A. Makhlouf, Paradigm of nonassociative Hom-algebras and Hom- superalgebras, Proceedings Jordan Structures in Algebra and Analysis Meet- ing, eds: J. Carmona Tapia, A. Morales Campoy, A. M. Peralta Pereira, M. I.
  • Ramirez Ivarez. Publishing House: Circulo Rojo (2010), 145-177.
  • A. Makhlouf and S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2008), 51-64.
  • D. Yau, Enveloping algebras of Hom-Lie algebras, J. Gen. Lie Theory Appl., 2 (2008), 95-108.
  • D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2009), 409-421.
  • D. Yau, Hom-Novikov algebras, J. Phys. A, 44 (2011), 085202.
  • D. Yau, Hom-Maltsev, Hom-alternative and Hom-Jordan algebras, Int. Elec- tron. J. Algebra, 11 (2012), 177-217.
  • D. Yau, Hom-power associative algebras, arXiv:1007.4118v1. A. Nourou Issa
  • D´epartement de Math´ematiques Universit´e d’Abomey-Calavi BP 4521 Cotonou 01, Benin e-mail: woraniss@yahoo.fr
There are 19 citations in total.

Details

Other ID JA26HD73YV
Journal Section Articles
Authors

A. Nourou Issa This is me

Publication Date December 1, 2013
Published in Issue Year 2013 Volume: 14 Issue: 14

Cite

APA Issa, A. N. (2013). SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra, 14(14), 1-9.
AMA Issa AN. SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS. IEJA. December 2013;14(14):1-9.
Chicago Issa, A. Nourou. “SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 14, no. 14 (December 2013): 1-9.
EndNote Issa AN (December 1, 2013) SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra 14 14 1–9.
IEEE A. N. Issa, “SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS”, IEJA, vol. 14, no. 14, pp. 1–9, 2013.
ISNAD Issa, A. Nourou. “SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 14/14 (December 2013), 1-9.
JAMA Issa AN. SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS. IEJA. 2013;14:1–9.
MLA Issa, A. Nourou. “SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra, vol. 14, no. 14, 2013, pp. 1-9.
Vancouver Issa AN. SOME CHARACTERIZATIONS OF HOM-LEIBNIZ ALGEBRAS. IEJA. 2013;14(14):1-9.