Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 648 - 675 2020-04-02

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

Abdelkader BEN HASSİNE [1] , Liangyun CHEN [2] , Juan Lİ [3]


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.
representations, derivations, deformations, T*-extensions, $\delta$-Bihom-Jordan-Lie algebras
  • [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.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0001-5440-8616
Yazar: Abdelkader BEN HASSİNE
Kurum: University of Bisha
Ülke: Saudi Arabia


Orcid: 0000-0002-2941-1087
Yazar: Liangyun CHEN
Kurum: Northeast Normal University
Ülke: China


Orcid: 0000-0002-0129-4544
Yazar: Juan Lİ
Kurum: Northeast Normal University
Ülke: China


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms588684, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {648 - 675}, doi = {10.15672/hujms.588684}, title = {Representations and \$T\^\{\\ast\}\$-extensions of \$\\delta\$-Bihom-Jordan-Lie algebras}, key = {cite}, author = {BEN HASSİNE, Abdelkader and CHEN, Liangyun and Lİ, Juan} }
APA BEN HASSİNE, A , CHEN, L , Lİ, J . (2020). Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 648-675 . DOI: 10.15672/hujms.588684
MLA BEN HASSİNE, A , CHEN, L , Lİ, J . "Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 648-675 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/588684>
Chicago BEN HASSİNE, A , CHEN, L , Lİ, J . "Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 648-675
RIS TY - JOUR T1 - Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras AU - Abdelkader BEN HASSİNE , Liangyun CHEN , Juan Lİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.588684 DO - 10.15672/hujms.588684 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 648 EP - 675 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.588684 UR - https://doi.org/10.15672/hujms.588684 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras %A Abdelkader BEN HASSİNE , Liangyun CHEN , Juan Lİ %T Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.588684 %U 10.15672/hujms.588684
ISNAD BEN HASSİNE, Abdelkader , CHEN, Liangyun , Lİ, Juan . "Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 648-675 . https://doi.org/10.15672/hujms.588684
AMA BEN HASSİNE A , CHEN L , Lİ J . Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 648-675.
Vancouver BEN HASSİNE A , CHEN L , Lİ J . Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 675-648.