We classify all simple supermodules over the queer Lie superalgebra q2 up to classification of equivalence classes of irreducible elements in a certain Euclidean ring.

A well known theorem of Duflo, the “annihilation theorem”, claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is centrally generated. For the Lie superalgebra osp(1, 2l), this result does not hold. In this article, we introduce a “correct” analogue of the centre for which the annihilation theorem does hold in the case osp(1, 2l). This sub...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

It shown that the supercommutator superalgebra of a right alternative is Bol superalgebra. Hom-Bol superalgebras are defined and it they closed under even self-morphisms. Any along with any self-morphism twisted into The Hom-alternative has natural structure. In order to prove this last result, Hom-Jordan-admissibility investigated next Hom-Jordan supertriple systems their connection Hom-Lie co...

We obtain a new free field realization of N = 2 super W3 algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra sl(3|2)(1) associated with a non-standard sl(2) embedding. After twisting and a similarity transformation, this W algebra can be identified as the extended topological conf...

On the basis of experimental work involving matrix computations , we conjecture that a criterion due to Bell for primeness of the universal enveloping algebra of a Lie superalgebra applies to the Cartan type Lie superalgebras W(n) for n = 3 but does not apply for odd n 5. The experiments lead to a rigorous proof, which we present.

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie superalgebra to an integral block of O for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of O.

A method is developed to construct irreducible representations(irreps) of the quantum supergroup U q (C(n + 1)) in a systematic fashion. It is shown that every finite dimensional irrep of this quantum supergroup at generic q is a deformation of a finite dimensional irrep of its underlying Lie superalgebra C(n + 1), and is essentially uniquely characterized by a highest weight. The character of ...

Abstract. The underlying field is of characteristic p > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an applicatio...