Saïd Benayadi
Lie superalgebras with some homogeneous structures.
Fri, 11/12/2010 - 16:01 — SomNambulAuthors: Saïd Benayadi, Imen Ayadi, Hedi Benamor
Subjects: Rings and Algebras
AbstractWe generalize to the case of Lie superalgebras the classical symplectic
double extension of symplectic Lie algebras introduced in [2]. We use this
concept to give an inductive description of nilpotent homogeneous-symplectic
Lie superalgebras. Several examples are included to show the existence of
homogeneous quadratic symplectic Lie superalgebras other than even-quadratic
even-symplectic considered in [6]. We study the structures of even (resp.
odd)-quadratic odd (resp.Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms.
Thu, 09/23/2010 - 15:01 — SomNambulAuthors: Abdenacer Makhlouf, Saïd Benayadi
Subjects: Rings and Algebras
AbstractThe aim of this paper is to introduce and study quadratic Hom-Lie algebras,
which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear
forms. We provide several constructions leading to examples and extend the
double extension theory to Hom-Lie algebras. We reduce the case where the twist
map is invertible to the study of involutive quadratic Lie algebras. We
establish a correspondence between the class of involutive quadratic Hom-Lie
algebras and quadratic simple Lie algebras with symmetric involution.
Centerless involutive quadratic Hom-Lie algebras are characterized.
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