Let H be a Heisenberg superalgebra. In this paper, the definition of biderivations and the properties of biderivations on Lie superalgebras are introduced. And some properties of biderivations on Heisenberg superalgebras are introduced by the definition of Heisenberg superalge-bras.

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

Using colored superanalysis and ε-Lie superalgebras, we build the minimal Poincaré superalgebra in the case of the Z n grading. We then build a representation of this algebra, and the corresponding Poincaré supergroup.

In this paper, the structure of parafermion vertex operator algebra associated to an integrable highest weight module for simple affine Lie superalgebra osp(1|2n) is studied. Particularly, we determine generators algebra.

On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications Abstract In a Wigner quantum mechanical model, with a solution in terms of the Lie superalgebra gl(1|n), one is faced with determining the eigenvalues and eigenvectors for an arbitrary self-adjoint odd element of gl(1|n) in any unitary irreducible representation W. We show that the eigenvalue p...

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra Bn = so(2n + 1); in the case of paraBose statistics they are associated with the Lie superalgebra B(0|n) = osp(1|2n). In a previous paper, a mathematical definition of “a generalized qu...

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from the Heisenberg subalgebra. also obtain deformations these for quantum Uqslˆ(m|n).

The orthosymplectic Lie superalgebra $$\mathfrak{osp}(1|\,2\ell)$$ is the closest superanalogue of standard algebras. We demonstrate that corresponding Toda chain an instance $$BC_\ell$$ chain. underlying reason for this relation discussed.

A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1, 2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not gene...