In this paper, we shall classify “quadratic” conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra. Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez–Jimbo, we construct inductive systems of Kirillov–Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yang...

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.

We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe cohomology complex by considering coefficient modules. Furthermore, we study the relationships between Lie-Rinehart its induced superalgebra. The deformations are considered via theory.

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...

Recently it was proposed that the Bagger-Lambert-Gustavsson theory with Nambu-Poisson structure describes an M5-brane in a three-form flux background. In this paper we investigate the superalgebra associated with this theory. We derive the central charges corresponding to M5-brane solitons in 3-form backgrounds. We also show that double dimensional reduction of the superalgebra gives rise to a ...

In arXiv:0806.0363 the worldvolume superalgebra of the N = 8 Bagger-Lambert theory was calculated. In this paper we derive the general form for the worldvolume superalgebra of the N = 6 Bagger-Lambert theory. For a particular choice of three-algebra we derive the superalgebra of the ABJM theory. We interpret the associated central charges in terms of BPS brane configurations. In particular we f...

We discuss an embedding of su(n) rank two antisymmetric supercharges in the su(2, 2|dn) superalgebra, where dn = n(n − 1)/2. describe algorithm to construct explicit form generators superalgebra.

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...

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.