On a complete rigid Leibniz non-Lie algebra in arbitrary dimension

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science
Google Scholar
Research Projects
Organizational Units
Journal Issue
We show that the only indecomposable solvable Leibniz non-Lie algebra L0 with nilradical of maximal nilpotence index is rigid in any dimension, andmoreover that it is complete, i.e., only possesses inner derivations. The possible contractions of L0 onto Lie algebras are obtained.
UCM subjects
Unesco subjects
A.M. Blokh, On a generalization of the notion of Lie algebra, Dokl. Akad. Nauk SSSR 165 (1965) 471–473. J.L. Loday, Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Enseign. Math. 39 (1993) 269–293. Sh.A. Ayupov, B.A. Omirov, On some classes of nilpotent Leibniz algebras, Sibirsk. Mat. Zh. 42 (2001) 18–29. Sh.A. Ayupov, B.A. Omirov, On Leibniz algebras, in: Proceedings of the Colloquium in Tashkent, 1997, Algebra and Operators Theory, pp. 1–13. J.M. Ancochea Bermúdez, J. Margalef, J. Samchez, Sur la réductibilité des variétés des lois d’algèbres de Leibniz complexes, J. Lie Theory 17 (2007) 617–624. D.W. Barnes, On Levi’s theorem for Leibniz algebras, Bull. Austral. Math. Soc. 86 (2012) 184–185. E. Nelson, Internal set theory: a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977) 1165–1198. J.M. Casas, M. Ladra, B.A. Omirov, I.A. Karimjanov, Classification of solvable Leibniz algebras with null-filiform nilradical, Linear and Multilinear Algebra 61 (2013) 758–774. R. Lutz, M. Goze, Nonstandard analysis: a practical guide with applications, Springer, NY, 1981. A. Fialowski, A. Mandal, Leibniz algebra deformations of a Lie algebra, J. Math. Phys. 49 (2008) 093512 I.S. Rakhimov, Kamel A.M. Atan, On contractions and invariants of Leibniz algebras, Bull. Malays.Math. Soc. 35 (2012) 557–565. R. Campoamor-Stursberg, A comment concerning cohomology and invariants of Lie algebras with respect to contractions and deformations, Phys. Lett. A 362 (2007) 360–367. A. Fialowski, A. Mandal, G. Mukherjee, Versal deformations of Leibniz algebras, K-Theory 3 (2008) 327–358. J.M. Ancochea, M. Goze, On the nonrationality of rigid Lie algebras, Proc. Amer. Math. Soc. 127 (1999) 2611–2618.