Extensions of Leibniz superalgebras

References

• Albeverio, S., Ayupov, S. A., Omirov, B. A. (2005). On nilpotent and simple Leibniz algebras. Commun. Algebra 33(1):159–172. DOI: 10.1081/AGB-200040932.
   Web of Science ®Google Scholar
• Albeverio, S., Omirov, B. A., Khudoyberdiyev, A. Kh. (2009). On the classification of complex Leibniz superalgebras with characteristic sequence (n−1,1|m1,…,mk) and nilindex n + m. J. Algebra Appl. 8(4):461–475.
   Web of Science ®Google Scholar
• Albeverio, S., Omirov, B. A., Rakhimov, I. S. (2005). Varieties of nilpotent complex Leibniz algebras of dimension less than five. Commun. Algebra 33(5):1575–1585. DOI: 10.1081/AGB-200061038.
   Web of Science ®Google Scholar
• Alekseevsky, D., Michor, P. W., Ruppert, W. (2004). Extensions of Lie algebras. arxiv:math/0005042v3.
   Google Scholar
• Alekseevsky, D., Michor, P. W., Ruppert, W. (2005). Extensions of super Lie algebras. J. Lie Theory 15(1):125–134.
   Web of Science ®Google Scholar
• Bai, Y., Chen, Y. (2020). Gröbner–Shirshov bases theory for Leibniz superalgebras. Commun. Algebra 50(8):3524–3542. DOI: 10.1080/00927872.2022.2036177.
   Web of Science ®Google Scholar
• Bloh, A. M. (1965). On a generalization of the concept of Lie algebra. Dokl. Akad. Nauk SSSR 165:471–473.
   Google Scholar
• Casas, J. M., Datuashvili, T. (2006). Noncommutative Leibniz-Poisson algebras. Commun. Algebra 34(7):2507–2530. DOI: 10.1080/00927870600651091.
   Web of Science ®Google Scholar
• Casas, J. M., Khmaladze, E., Ladra, M. (2013). Low-dimensional non-abelian Leibniz cohomology. Forum Math. 25(3):443–469.
   Web of Science ®Google Scholar
• Chen, Y. (2008). Gröbner-Shirshov basis for Schreier extensions of groups. Commun. Algebra 36(5):1609–1625. DOI: 10.1080/00927870701869899.
   Web of Science ®Google Scholar
• Chen, Y., Qiu, J. Extensions of associative and Lie algebras via Gröbner-Shirshov bases method. Algebra Colloquium (to appear). arXiv:1603.01454.
   Google Scholar
• Feldvoss, J., Wagemann, F. (2021). On Leibniz cohomology. J. Algebra 569:276–317. DOI: 10.1016/j.jalgebra.2020.11.003.
   Web of Science ®Google Scholar
• Felipe, R., López-Reyes, N., Ongay, F. (2003). R-matrices for Leibniz algebras. Lett. Math. Phys. 63(2):157–164.
   Web of Science ®Google Scholar
• Fialowski, A., Penkava, M. (2014). Extensions of associative algebras. Commun. Contemp. Math. 16(3):1450014(29pp). DOI: 10.1142/S021919971450014X.
   Web of Science ®Google Scholar
• Gómez, J. R., Khudoyberdiyev, A. Kh., Omirov, B. A. (2010). The classification of Leibniz superalgebras of nilindex n+m(m≠0) . J. Algebra 324:2786–2803.
   Web of Science ®Google Scholar
• Hall, M. (1959). The Theory of Groups. New York: The Macmillan Company.
   Google Scholar
• Hu, N., Liu, D., Zhu, L. (2005). Leibniz superalgebras graded by finite root systems. arXiv:math/0510544.
   Google Scholar
• Hu, N., Pei, Y., Liu, D. (2007). A cohomological characterization of Leibniz central extensions of Lie algebras. Proc. Amer. Math. Soc. 136(2):437–447.
   Web of Science ®Google Scholar
• Kac, V. G. (1977). Lie superalgebras. Adv. Math. 26(1):8–96.
   Web of Science ®Google Scholar
• Kurdachenko, L. A., Subbotin, I. Y., Yashchuk, V. S. (2020). Some antipodes of ideals in Leibniz algebras. J. Algebra Appl. 19(6):2050113(14pp). DOI: 10.1142/S0219498820501133.
   Web of Science ®Google Scholar
• Liu, D. (2005). Steinberg-Leibniz algebras and superalgebras. J. Algebra 283(1):199–221. DOI: 10.1016/j.jalgebra.2004.08.005.
   Web of Science ®Google Scholar
• Liu, D., Hu, N. (2006). Leibniz superalgebras and central extensions. J. Algebra Appl. 05(06):765–780. DOI: 10.1142/S0219498806001983.
   Google Scholar
• Loday, J.-L. (1993). Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math. 39:269–293.
   Google Scholar
• Loday, J.-L., Pirashvili, T. (1993). Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296(1):139–158.
   Web of Science ®Google Scholar
• Martín, A. J. C., Sánchez-Delgado, J. M. (2013). On split Leibniz superalgebras. Linear Algebra Appl. 438(12):4709–4725.
   Web of Science ®Google Scholar
• Mason, G., Yamskulna, G. (2013). Leibniz algebras and Lie algebras. Symmetry, Integr. Geom.: Methods Appl. 9(4):063(10pp).
   Google Scholar
• Militaru, G. (2015). The global extension problem, co-flag and metabelian Leibniz algebras. Linear Multilinear Algebra 63(3):601–621. DOI: 10.1080/03081087.2014.891587.
   Web of Science ®Google Scholar
• Muratova, Kh. A., Khudoyberdiyev, A. Kh. (2020). On Leibniz superalgebras which even part is sl2 . J. Algebra Appl. 20(9):2150161.
   Google Scholar