We prove denominator identities for the periplectic Lie superalgebra p ( n ) , thereby completing problem of finding all simple classical finite-dimensional superalgebras.

We study of the category O for the queer Lie superalgebra q(n), and the corresponding block decomposition induced by infinitesimal central characters. In particular, we show that the so-called typical blocks correspond to standardly stratified algebras, in the sense of Cline, Parshall and Scott. By standard arguments for Lie algebras, modified to the superalgebra situation, we prove that these ...

The character formula of any finite dimensional irreducible module Lλ for Lie superalgebra osp(n|2) is computed. As a by-product, the decomposition of tensor module Lλ ⊗ C n|2, where Cn|2 is the natural representation, is obtained.

Let e be an arbitrary even nilpotent element in the general linear Lie superalgebra glM|N and let We associated finite W-superalgebra. Ym|n super Yangian to glm|n. A subalgebra of Ym|n, called shifted denoted by Ym|n(σ), is defined studied. Moreover, explicit isomorphism between a quotient Ym|n(σ) established.

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...

We classify irreducible representations of finite W-algebra for the queer Lie superalgebra Q(n) associated with principal nilpotent coadjoint orbits. use this classification and our previous results to obtain a finite-dimensional super Yangian YQ(1).

In this paper, the intuitionistic fuzzy Lie sub-superalgebras and ideals of Lie superalgebras are studied further. We define the intuitionistic fuzzy quotient Lie superalgebra by an intuitionistic fuzzy Lie ideal and prove that it is a Lie superalgebra. The intuitionistic fuzzy set of quotient Lie superalgebra is also considered. Finally, solvable intuitionistic fuzzy Lie ideals and nilpotent i...

We investigate cohomological support varieties for finite-dimensional Lie superalgebras defined over fields of odd characteristic. Verifying a conjecture from our previous work, we show the variety supermodule can be realized as an explicit subset nullcone underlying superalgebra. also is zero if and only finite projective dimension. As consequence, obtain positive characteristic version theore...

Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [8]. This leads to a classification problem. For example, in [4], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...