We determine the structure of the ∗-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of sl(4, C) with the full special linear superalgebras of some graded vector spaces isotypical with respect to a natural ac...

Consider the complex matrix Lie superalgebra glN|N with the standard generators Eij where i, j = ±1 , . . . ,±N . Define an involutory automorphism η of glN|N by η (Eij) = E−i,−j . The twisted polynomial current Lie superalgebra g = {X(u) ∈ glN|N [u] : η (X(u)) = X(−u) } has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra U(g) as a co-Poisson Hopf superalge...

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...

We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe cohomology complex by considering coefficient modules. Furthermore, we study the relationships between Lie-Rinehart its induced superalgebra. The deformations are considered via theory.

We introduce a new quantum group which is a quantization of the enveloping superalgebra of a twisted affine Lie superalgebra of type Q. We study generators and relations for superalgebras in the finite and twisted affine cases, and also universal central extensions. Afterwards, we apply the FRT formalism to a certain solution of the quantum Yang-Baxter equation to define that new quantum group ...

Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g ⊕ g+, and let s and t be commuting formal variables commuting with g. We prove that the map C : sg[[s, t]] × tg+[[s, t]] −→ sg[[s, t]] ⊕ tg+[[s, t]] defined by the Campbell-Baker-Hausdorff formula and given by e − e + = eC(sg ,tg) for g ∈ g[[s, t]] is a bijection, as is well known when g ...

The aim of this work is to prove a technical result, that had been stated by Boyallian, Kac and Liberati \cite{ck6}, on the degree singular vectors finite Verma modules over exceptional Lie superalgebra $E(1,6)$ isomorphic annihilation associated with conformal $CK_{6}$.

In our recent paper [DSK11] we computed the dimension of the variational Poisson cohomology H•K(V) for any quasiconstant coefficient l × l matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the Z-graded Lie sup...