On nilpotent and simple Leibniz algebras

Communications in Algebra

Volumn 33, Issue 1, 2005, Pages 159-172

  Albeverio, S ^a   Ayupov, Sh A ^b   Omirov, B A ^b  

^a UNIVERSITY OF BONN   (Germany)

^b S YU YUNUSOV INSTITUTE OF THE CHEMISTRY OF PLANT SUBSTANCES   (Uzbekistan)

Author keywords

Engel's conditions; Leibniz algebras; Leibniz superalgebras; Lie algebras; Nilpotent; Simple Leibniz algebras; Solvable

Indexed keywords

EID: 27844472052     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1081/AGB-200040932     Document Type: Article

References (14)

1. Abdykassymova, S., Dzhumadil'daev, A. (2000). Simple Leibniz algebras of rank 1. Abstracts Presented to the IX International Conference of the Representation Theory of Algebras, Beijing, pp. 17-18.
2. Abdykassymova, S. (2001). Leibniz algebras of rank 1 in the characteristic p. Ph.D. thesis, Almaty State University.
3. Ayupov, Sh. A., Omirov, B. A. (1998). On Leibniz algebras. Algebra and Operators Theory. Proceedings of the Colloquium in Tashkent 1997. Kluwer, pp. 1-13.
4. Ayupov, Sh. A., Omirov, B. A. (1999). On 3-dimensional Leibniz algebras. Uzbek Math. J. 1:9-14.
5. Ayupov, Sh. A., Omirov, B. A. (2001). On some classes of nilpotent Leibniz algebras. Siberian Math. Journal 42(1):18-29.
6. Bakhturin, Yu. A. (1985). Identities in Lie algebras. Moscow: Nauka.
7. Bloch, A. (1965). On a generalization of Lie algebra notion. Math, in USSR Doklady 165(3):471-473.
8. Filippov, V. T. (1975). On Maltzev algebras, satisfying Engel condition. Algebra i Logika 14(4):441-455.
9. Jacobson, N. (1962). Lie algebras. New York: Wiley Interscience.
10. Latyshev, V. N. (1963). On zero divisors and nilelements in Lie algebras. Siberian Math. J. 4(4):830-836.
11. Livernet, M (1998). Rational homotopy of Leibniz algebras. Manuscripta Math. 96:295-315.
12. Loday, J.-L. (1993). Une version non commutative des algébres de Lie: les algébres de Leibniz. L'Ens. Math. 39:269-293.
13. Loday, J.-L., Pirashvili, T. (1993). Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296:139-158.
14. Zelmanov, E. I. (1987). On Engel Lie algebras. Math. USSR Doklady 292:265-268.