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Year 2020, Volume: 49 Issue: 2, 648 - 675, 02.04.2020
https://doi.org/10.15672/hujms.588684

Abstract

References

  • [1] S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76, 38–60, 2014.
  • [2] M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, Acta Math. Univ. Comenian. (N.S.) 66 (2), 151–201, 1997.
  • [3] Y. Cheng and H. Qi, Representations of Bihom-Lie algebras, arXiv:1610.04302.
  • [4] G. Graziani, A. Makhlouf, C. Menini, and F. Panaite, Bihom-associative algebras, Bihom-Lie algebras and Bihom-bialgebras, SIGMA Symmetry Integrability Geom. Methods Appl. (11), Paper 086, 34 pp, 2015.
  • [5] J. Hartwig, D. Larsson and S. Silvestrov, Deformations of Lie algebras using σ- derivations, J. Algebra 295 (2), 314–361, 2006.
  • [6] A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  • [7] S. Okubo and N. Kamiya, Jordan Lie superalgebra and Jordan Lie triple system, J. Algebra 198 (2), 388–411, 1997.
  • [8] L. Qian, J. Zhou, and L. Chen, Engel’s theorem for Jordan-Lie algebras and its applications, Chinese Ann. Math. Ser. A 33 (5), 517–526, 2012 (in Chinese).
  • [9] S. Wang and S. Guo, Bihom-Lie superalgebra structures, arXiv:1610.02290.
  • [10] J. Zhao, L. Chen, and L. Ma, Representations and $T^\ast$-extensions of Hom-Jordan-Lie Algebras, Comm. Algebra 44 (7), 2786–2812, 2016.

Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras

Year 2020, Volume: 49 Issue: 2, 648 - 675, 02.04.2020
https://doi.org/10.15672/hujms.588684

Abstract

The purpose of this article is to study representations of $\delta$-Bihom-Jordan-Lie algebras. In particular, adjoint representations, trivial representations, deformations, $T^\ast$-extensions of $\delta$-Bihom-Jordan-Lie algebras are studied in detail. Derivations and central extensions of $\delta$-Bihom-Jordan-Lie algebras are also discussed as an application.

References

  • [1] S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76, 38–60, 2014.
  • [2] M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, Acta Math. Univ. Comenian. (N.S.) 66 (2), 151–201, 1997.
  • [3] Y. Cheng and H. Qi, Representations of Bihom-Lie algebras, arXiv:1610.04302.
  • [4] G. Graziani, A. Makhlouf, C. Menini, and F. Panaite, Bihom-associative algebras, Bihom-Lie algebras and Bihom-bialgebras, SIGMA Symmetry Integrability Geom. Methods Appl. (11), Paper 086, 34 pp, 2015.
  • [5] J. Hartwig, D. Larsson and S. Silvestrov, Deformations of Lie algebras using σ- derivations, J. Algebra 295 (2), 314–361, 2006.
  • [6] A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  • [7] S. Okubo and N. Kamiya, Jordan Lie superalgebra and Jordan Lie triple system, J. Algebra 198 (2), 388–411, 1997.
  • [8] L. Qian, J. Zhou, and L. Chen, Engel’s theorem for Jordan-Lie algebras and its applications, Chinese Ann. Math. Ser. A 33 (5), 517–526, 2012 (in Chinese).
  • [9] S. Wang and S. Guo, Bihom-Lie superalgebra structures, arXiv:1610.02290.
  • [10] J. Zhao, L. Chen, and L. Ma, Representations and $T^\ast$-extensions of Hom-Jordan-Lie Algebras, Comm. Algebra 44 (7), 2786–2812, 2016.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Abdelkader Ben Hassine 0000-0001-5440-8616

Liangyun Chen 0000-0002-2941-1087

Juan Li This is me 0000-0002-0129-4544

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Ben Hassine, A., Chen, L., & Li, J. (2020). Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics, 49(2), 648-675. https://doi.org/10.15672/hujms.588684
AMA Ben Hassine A, Chen L, Li J. Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):648-675. doi:10.15672/hujms.588684
Chicago Ben Hassine, Abdelkader, Liangyun Chen, and Juan Li. “Representations and $T^{\ast}$-Extensions of $\delta$-Bihom-Jordan-Lie Algebras”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 648-75. https://doi.org/10.15672/hujms.588684.
EndNote Ben Hassine A, Chen L, Li J (April 1, 2020) Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics 49 2 648–675.
IEEE A. Ben Hassine, L. Chen, and J. Li, “Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 648–675, 2020, doi: 10.15672/hujms.588684.
ISNAD Ben Hassine, Abdelkader et al. “Representations and $T^{\ast}$-Extensions of $\delta$-Bihom-Jordan-Lie Algebras”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 648-675. https://doi.org/10.15672/hujms.588684.
JAMA Ben Hassine A, Chen L, Li J. Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020;49:648–675.
MLA Ben Hassine, Abdelkader et al. “Representations and $T^{\ast}$-Extensions of $\delta$-Bihom-Jordan-Lie Algebras”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 648-75, doi:10.15672/hujms.588684.
Vancouver Ben Hassine A, Chen L, Li J. Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):648-75.