The universal central extensions and their extension kernels of the matrix Lie superalgebra sl(m, n,A), the Steinberg Lie superalgebra st(m, n,A) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with [MP]) using the first Hochschild homology and the first cyclic homology group.

Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...

Suppose the ground field $$\mathbb{F}$$ is an algebraically closed characteristic of p > 2. In this paper, we investigate restricted cohomology theory Lie superalgebras. Algebraic interpretations low dimensional superalgebra are given. We show that there a family model filiform $$L_{p,p}^\lambda$$ structures parameterized by elements $$\lambda \in {\mathbb{F}^p}$$ . explicitly describe both 1-d...

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...