Simple associative superalgebra with 2 independent supertraces is presented. Its commutant is a simple Lie superalgebra which has at least 2 independent invariant bilinear forms.

The N=2 superconformal (or super-Virasoro) algebras in two dimensions are three complex Lie superalgebras: the Neveu-Schwarz superalgebra [1], the Ramond superal-gebra [1], the twisted superalgebra [2], which are denoted as A, P, T , resp., or G when a statement holds for all three superalgebras. They have the following nontrivial super-Lie brackets :

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.

We study central extensions of the Lie superalgebra sln(A) when A is a Z/2Z-graded superalgebra over a commutative ring K. Steinberg Lie superalgebras and their central extensions play an essential role. We use a Z/2Z-graded version of cyclic homology to study the center of the extensions in question.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

Recently, the classical Freudenthal Magic Square has been extended over fields of characteristic 3 with two more rows and columns filled with (mostly simple) Lie superalgebras specific of this characteristic. This Supermagic Square will be reviewed and some of the simple Lie superalgebras that appear will be shown to be isomorphic to the Tits-Kantor-Koecher Lie superalgebras of some Jordan supe...

The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra a...

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one paramete...

A superconformal algebra is a simple complex Lie superalgebra g spanned by the coefficients of a finite family of pairwise local fields a(z) = ∑ n∈Z a(n)z , one of which is the Virasoro field L(z), [3, 8, 11]. Superconformal algebras play an important role in the string theory and conformal field theory. The Lie superalgebras K(N) of contact vector fields with Laurent polynomials as coefficient...