The global extension problem, co-flag and metabelian Leibniz algebras

References

• Bloh AM. On a generalization of the concept of Lie algebra. Dokl. Akad. Nauk SSSR. 1965;165:471–473.
   Google Scholar
• Loday J-L. Une version non commutative des algèbres de Lie: les algèbres de Leibniz [A noncommutative version of Lie algebras: the Leibniz algebras]. L’Enseignement Math. 1993;39:269–293.
   Google Scholar
• Cuvier C. Algèbres de Leibniz: définitions, propriétés [Leibniz algebras: definitions, properties]. Ann. Scient. Ec. Norm. Sup. 1994;27:1–45.
   Web of Science ®Google Scholar
• Loday J-L, Pirashvili T. Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 1993;296:139–158.
   Web of Science ®Google Scholar
• Albeverio S, Omirov BA, Rakhimov IS. Varieties of nilpotent complex Leibniz algebras of dimension less than five. Comm. Algebra. 2005;33:1575–1585.
   Web of Science ®Google Scholar
• Albeverio S, Ayupov ShA, Omirov BA, Khudoyberdiyev AKh. n-dimensional filiform Leibniz algebras of length (n − 1) and their derivations. J. Algebra. 2008;319:2471–2488.
   Web of Science ®Google Scholar
• Barnes D. On Levi’s theorem for Leibniz algebras. Bull. Australian Math. Soc. 2012;86:184–185.
   Web of Science ®Google Scholar
• Calderon Martin AJ, Sanchez Delgado JM. On split Leibniz algebras. Linear Algebra Appl. 2012;436:1651–1663.
   Web of Science ®Google Scholar
• Camacho LM, Cañete EM, Gómez JR, Redjepov ShB. Leibniz algebras of nilindex n − 3 with characteristic sequence (n − 3,2,1). Linear Algebra Appl. 2013;438:1832–1851.
   Web of Science ®Google Scholar
• Canete EM, Khudoyberdiyev AKh. The classification of 4-dimensional Leibniz algebras. Linear Algebra Appl. 2013;439:273–288.
   Web of Science ®Google Scholar
• Casas JM, Corral N. On universal central extensions of Leibniz algebras. Comm. Algebra. 2009;37:2104–2120.
   Web of Science ®Google Scholar
• Casasa JM, Ladrab M, Omirov BA, Karimjanov IA. Classification of solvable Leibniz algebras with null-filiform nilradical. Linear Multilinear Algebra. 2013;61:758–774.
   Web of Science ®Google Scholar
• Casas JM, Insua MA, Ladra M, Ladra S. An algorithm for the classification of 3-dimensional complex Leibniz algebras. Linear Algebra Appl. 2012;436:3747–3756.
   Web of Science ®Google Scholar
• Casas JM, Datuashvili T. Noncommutative Leibniz-Poisson algebras. Comm. Algebra. 2006;34:2507–2530.
   Web of Science ®Google Scholar
• Fialowski M, Mandal A. Leibniz algebra deformations of a Lie algebra. J. Math. Phys. 2008;49:093512. 11 p.
   Google Scholar
• Gorbatsevich VV. On some basic properties of Leibniz algebras. arXiv:1302.3345.
   Google Scholar
• Hu N, Pei Y, Liu D. A cohomological characterization of Leibniz central extensions of Lie algebras. Proc. AMS. 2008;136:437–447.
   Web of Science ®Google Scholar
• Kinyon MK, Weinstein A. Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces. Amer. J. Math. 2001;123:525–550.
   Web of Science ®Google Scholar
• Kosmann-Schwarzbach Y. Courant algebroids. A short history. SIGMA. 2013;9:014. 8 p.
   Google Scholar
• Mason G, Yamskulna G. Leibniz algebras and Lie algebras. SIGMA. 2013;9:063. 10 p.
   Google Scholar
• Rakhimov IS, Hassan MA. On isomorphism criteria for Leibniz central extensions of a linear deformation of μn. Internat. J. Algebra Comput. 2011;21:715–729.
   Web of Science ®Google Scholar
• Rakhimov IS, Said Husain SK. Classification of a subclass of nilpotent Leibniz algebras. Linear Multilinear Algebra. 2011;59:339–354.
   Web of Science ®Google Scholar
• Agore AL, Militaru G. Unified products for Leibniz algebras. Applications. Linear Algebra Appl. 2013;439:2609–2633.
   Web of Science ®Google Scholar
• Agore AL, Militaru G. Extending structures for Lie algebras. Monatshefte für Mathematik. doi: 10.1007/s00605-013-0537-7. arXiv:1301.5442.
   Web of Science ®Google Scholar
• Agore AL, Militaru G. Extending structures II: the quantum version. J. Algebra. 2011;336:321–341.
   Web of Science ®Google Scholar
• Agore AL, Militaru G. Extending structures I: the level of groups. Algebr. Represent. Theory. doi: 10.1007/s10468-013-9420-4. arXiv:1011.1633.
   Web of Science ®Google Scholar
• Agore AL, Militaru G. Classifying complements for Hopf algebras and Lie algebras. J. Algebra. 2013;391:193–208.
   Web of Science ®Google Scholar
• Kurdiani R, Pirashvilli T. A Leibniz algebra structure on the second tensor power. J. Lie Theory. 2002;12:583–596.
   Web of Science ®Google Scholar