In this work, differential geometry of the Z3-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained. E-mail: [email protected]

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.

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.

Let (g, k) be a reductive symmetric superpair of even type, i.e. so that there exists an even Cartan subspace a ⊂ p. The restriction map S(p) → S(a) where W = W (g0 : a) is the Weyl group, is injective. We determine its image explicitly. In particular, our theorem applies to the case of a symmetric superpair of group type, i.e. (k ⊕ k, k) with the flip involution where k is a classical Lie supe...

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...

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.

We classify the blocks and compute Verma flags of tilting projective modules in BGG category O for exceptional Lie superalgebra G(3). The injective are classified. also Jordan–Hölder multiplicities O.