We suggest a programming realization of an algorithm for a verification of a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan procedure for a quadratic superalgebra and whose elements are realized as a formal power series with respect to noncommuting elements. To this end, we propo...

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 provide a classification of the IIB Dpand NSp-branes in which the brane action exists due to a non-trivial class of the Chevalley-Eilenberg cohomology of free differential algebras. We then present a new geometric formulation of the IIB Dpand NSp-branes (p ≤ 5) in which the manifestly superinvariant Wess-Zumino terms are constructed in terms of the supersymmetric currents. The supercurrents ...

We propose an extension of the su(2, 2|4) superalgebra to incorporate the F1/D1 string charges in type IIB string theory on the AdS5 × S 5 background, or the electro-magnetic charges in the dual super Yang-Mills theory. With the charges introduced, the superalgebra inevitably undergoes a noncentral extension, as noted recently in [1]. After developing a group theoretical method of obtaining the...

The two–parametric quantum superalgebra U p,q [gl(2/2)] and its representations are considered. All finite–dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and non–typical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superal-gebra gl(2/2)...

In the paper, we extend the definition of generalized derivations to superalgebras and prove that a generalized superderivation g on a prime superalgebra A is represented as g(x) = ax + d(x) for all x ∈ A, where a is an element of Qmr (the maximal right ring of quotients of A) and d is a superderivation on A. Using the result we study two generalized superderivations when their product is also ...

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN . For each M = 1 ,2 , . . . denote by A M N the centralizer of qM ⊂ qN+M in the associative superalgebra U(qN+M ) . We construct a sequence of surjective homomorphisms U(qN ) ← A 1 N ← A 2 N ← . . . . We describe the inverse limit of the sequence of centralizer algebras A1N ,A 2 N , . . . in terms ...