Para-Fermi statistics and Fermi statistics are known to be associated with particular representations of the Lie algebra so(2n+1)≡ Bn. Similarly paraBose and Bose statistics are related with the Lie superalgebra osp(1|2n)≡ B(0|n). We develop an algebraical framework for the generalization of quantum statistics based on the Lie algebras An, Bn, Cn and Dn.

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 ...

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...

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.

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...