RT Journal Article T1 On a nilpotent Lie superalgebra which generalizes Qn A1 Ancochea Bermúdez, José María A1 Campoamor-Stursberg, Rutwig AB In [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequenceof the centralizer property. Certain central extensions ofQn which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras PB Universidad Complutense de Madrid SN 1988-2807 YR 2002 FD 2002 LK https://hdl.handle.net/20.500.14352/58404 UL https://hdl.handle.net/20.500.14352/58404 LA eng NO Yu. A. Bakhturin, V. S. Drewnski, The identities of solvable colored Lie algebras, Algebra i Logika, 26 (1987), 403-418.K. Bauwens and L. Le Bruiyn, Some remarks on solvable Lie superalgebras, J. Pure Appl. Algebra, 99 (1995), 113-134.M. Boral, N. Ekizi and Y. Ünlü, On finitely generated free nilpotent Lie superalgebras of class <5, Algebras Groups Geom., 12 (1995), no. 3, 247-254.R. Campoamor, J. M. Ancochea, On certain families of naturally graded Lie algebras, J. Pure Appl. Algebra, to appear.L. Corwin, Y. Ne'eman and S. Sternberg, Graded Lie algebras in matehmatics and physics, Rev. Mod. Phys., 47 (1975), 573-603.M. Gilg, Superalgèbres de Lie nilpotentes, Ph. D. Thesis, Mulhouse 2000.M. Gilg, Low-dimensional filiform Lie superalgebras, Rev. Mat. Compl. XIV (2001), 463-478.A. Hegazi, Classification of nilotent Lie superalgebras of dimension five I, Internat. J. Theoret. Phys., 38 (1999), no. 6, 1735-1739.A. Hegazi, Classification of nilotent Lie superalgebras of dimension five II, Internat. J. Theoret. Phys., 38 (1999), no. 10, 2681-2693.A. Hegazi, A classification of nilotent Lie superalgebras of dimension five I, Panamer. Math. J., 10 (2000), no. 1, 75-93.V. G. Kac, Lie superalgbras, Adv. Math., 26 (1977), 8-96.M. Scheunert, The theory of Lie superlagebras, L.N.M 716 (1978).M. Vergne, Cohomologie des algèbres de Lie nilpotente. Applications a l’étude de la variété des algèbres de Lie nilpotentes, Bull. Soc. Math. France, 78 (1970), 81-116. DS Docta Complutense RD 4 may 2024