EN
Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras
Abstract
The purpose of this article is to study Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. We show that the deformation generated by a Bihom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^*$-extensions of Bihom-Lie superalgebras and show that $T^*$-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. In particular, we discuss the equivalence of $T^*$-extensions.
Keywords
References
- K. Abdaoui, F. Ammar and A. Makhlouf, Constructions and cohomology of Hom-Lie color algebras, Comm. Algebra 43 (11), 4581-4612, 2015.
- F. Ammar, I. Ayadi, S. Mabrouk and A. Makhlouf, Quadratic color Hom-Lie algebras, arXiv:1204.5155.
- F. Ammar Z. Ejbehi and A. Makhlouf, Cohomology and deformations of Hom- algebras, J. Lie Theory 21 (4), 813-836, 2011.
- F. Ammar and A. Makhlouf, Hom-Lie superalgebras and Hom-Lie admissible super- algebras, J. Algebra 324 (7), 1513-1528, 2010.
- F. Ammar, A. Makhlouf and N. Saadoui, Cohomology of Hom-Lie superalgebras and q-deforemed Witt superalgebra, Czechoslovak Math. J. 63(138) (3), 721-761, 2013.
- M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, Acta Math. Univ. Comenian. (N.S.) 66 (2), 151-201, 1997.
- I. Bajo, S. Benayadi and A. Medina, Symplectic structures on quadratic Lie algebras, J. Algebra 316 (1), 174-188, 2007.
- S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegen- erate bilinear forms, J. Geom. Phys. 76, 38-60, 2014.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
June 15, 2019
Submission Date
October 19, 2017
Acceptance Date
January 12, 2018
Published in Issue
Year 2019 Volume: 48 Number: 3
APA
Li, J., Chen, L., & Sun, B. (2019). Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. Hacettepe Journal of Mathematics and Statistics, 48(3), 785-799. https://izlik.org/JA99FC22RZ
AMA
1.Li J, Chen L, Sun B. Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):785-799. https://izlik.org/JA99FC22RZ
Chicago
Li, Juan, Liangyun Chen, and Bing Sun. 2019. “Bihom-Nijienhuis Operators and $T^*$-Extensions of Bihom-Lie Superalgebras”. Hacettepe Journal of Mathematics and Statistics 48 (3): 785-99. https://izlik.org/JA99FC22RZ.
EndNote
Li J, Chen L, Sun B (June 1, 2019) Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. Hacettepe Journal of Mathematics and Statistics 48 3 785–799.
IEEE
[1]J. Li, L. Chen, and B. Sun, “Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 785–799, June 2019, [Online]. Available: https://izlik.org/JA99FC22RZ
ISNAD
Li, Juan - Chen, Liangyun - Sun, Bing. “Bihom-Nijienhuis Operators and $T^*$-Extensions of Bihom-Lie Superalgebras”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 1, 2019): 785-799. https://izlik.org/JA99FC22RZ.
JAMA
1.Li J, Chen L, Sun B. Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. Hacettepe Journal of Mathematics and Statistics. 2019;48:785–799.
MLA
Li, Juan, et al. “Bihom-Nijienhuis Operators and $T^*$-Extensions of Bihom-Lie Superalgebras”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, June 2019, pp. 785-99, https://izlik.org/JA99FC22RZ.
Vancouver
1.Juan Li, Liangyun Chen, Bing Sun. Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. Hacettepe Journal of Mathematics and Statistics [Internet]. 2019 Jun. 1;48(3):785-99. Available from: https://izlik.org/JA99FC22RZ