References
- Loday J-L. Une version non commutative des alge`bres de Lie: les alge`bres de Leibniz. Enseign Math. 1993;39(3–4):269–293.
- Albeverio ShA, Ayupov ShA, Omirov BA. On nilpotent and simple Leibniz algebras. Comm Algebra. 2005;33(1):159–172. doi: 10.1081/AGB-200040932
- Ayupov ShA, Camacho LM, Khudoyberdiyev AK, Omirov BA. Leibniz algebras associated with representations of filiform Lie algebras. J Geom Phys. 2015;98:181–195. doi: 10.1016/j.geomphys.2015.08.002
- Ayupov ShA, Omirov BA. On Leibniz algebras, algebra and operator theory (Tashkent, 1997). Dordrecht: Kluwer Academic Publishers; 1998; p. 1–12.
- Ayupov SA, Kudaybergenov KK, Omirov BA, Zhao K. Semisimple Leibniz algebras and their derivations and automorphisms. arxiv. 1708.08082v1.
- Adashev JQ, Omirov BA, Uguz S. Leibniz algebras associated with representations of Euclidean Lie algebra. arxiv. 2016;1607.04949.
- Albeverio SA, Ayupov ShA, Omirov BA. Cartan subalgebras weight spaces, and criterion of solvability of finite dimensional Leibniz algebras. Rev Mat Complut. 2006;19(1):183–195.
- Barnes D. On Engel's theorem for Leibniz algebras. Comm Algebra. 2012;40(4):1388–1389. doi: 10.1080/00927872.2010.551532
- Barnes D. On Levi's theorem for Leibniz algebra. Bull Aus Math Soc. 2012;86:184–185. doi: 10.1017/S0004972711002954
- Bosko L, Hedges A, Hird JT, et al. Jacobson's refinement of Engel's theorem for Leibniz algebras. Involve. 2011;4(3):293–296. doi: 10.2140/involve.2011.4.293
- Camacho LM, Karimjanov IA, Ladra M, Omirov BA. Leibniz algebras constructed by representations of General Diamond Lie algebras. Bull Malays Math Sci Soc. 2017. doi:10.1007/s40840-017-0541-5.
- Calderón AJ, Camacho LM, Omirov BA. Leibniz algebras of Heisenberg type. J Algebra. 2016;452:427–447. doi: 10.1016/j.jalgebra.2015.12.018
- Omirov B. Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras. J Algebra. 2006;302(2):887–896. doi: 10.1016/j.jalgebra.2006.01.004
- Uguz S, Karimjanov IA, Omirov BA. Leibniz algebras associated with representations of the Diamond Lie algebra. Algebr Represent Theor. 2017;20:175–195. doi: 10.1007/s10468-016-9636-1
- Jacobson N. Lie algebras. New York: Interscience Publishers, Wiley; 1962; 340p.
- Humphreys JE. Introduction to Lie algebras and representation theory. New York: Springer-Verlag; 1972.
- Cartan E. Les groupes de transformations continus infinis, simples. Ann Sci Ecole Norm Sup. 1909;26:93–161. doi: 10.24033/asens.603
- Kac V, Raina A. Bombay lectures on highest weight representations of infinite-dimensional Lie algebras. Singapore: World Scientific; 1987.
- Eswara Rao S. Representations of Witt algebras. Publ Res Inst Math Sci. 1994;30:191–201. doi: 10.2977/prims/1195166128
- Lü R, Guo X, Zhao K. Irreducible modules over the Virasoro algebra. Doc Math. 2011;16:709–721.
- Zhao K. Weight modules over generalized Witt algebras with 1-dimensional weight spaces. Forum Math. 2004;16:725–748. doi: 10.1515/form.2004.034
- Loday J-L, Pirashvili T. Universal envoloping algebras of Leibniz algebras and (co)homology. Math Ann. 1993;296:139–158. 748. doi: 10.1007/BF01445099
- Ecker J, Schlichenmaier M. The vanishing of low-dimensional cohomology groups of the Witt and the Virasoro algebra. arXiv:1707.06106v1.
- Fialowski A, Schlichenmaier M. Global deformations of the Witt algebra of Krichever-Noviker type. Commun Contemporary Math. 2003;5(6):921–945. doi: 10.1142/S0219199703001208