We prove that the natural map from the center of the affine Sergeev superalgebra to the even center of any cyclotomic Sergeev superalgebra of odd level is surjective, hence that the even center of a cyclotomic Sergeev superalgebra of odd level consists of symmetric functions in the squares of its polynomial generators.

We prove that the super star product on a Poisson Lie supergroup leads to the structure of quantum superalgebra ( triangular Hopf superalgebra) on the super quantized enveloping algebra of the Lie superalgebra of the Lie supergroup and that equivalents super star products generate isomorphic quantum superalgebras.

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...

We obtain the pullback to the F-string worldsheet of the R⊗R gauge potential bR by considering a map which transforms the F-string superalgebra to the D-string superalgebra. In addition, it is shown that bR on the worldsheet is obtained by starting with a superalgebra, which is obtained by interchanging new fermionic generators, Zα and Z̃α, in the F-string superalgebra. Interchanging new fermion...

Spacetime superalgebras with 64 or less number of real supercharges, containing the type IIB Poincaré superalgebra in (9, 1) dimensions and the N = 1 Poincaré superalgebra in (10, 1) are considered. The restriction D ≤ 14, and two distinct possibilities arise: The N = (1, 0) superalgebra in (11, 3) dimensions, and the N = (2, 0) superalgebra in (10, 2) dimensions. Emphasizing the former, we des...

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...

The paper concerns two versions of the notion of real forms of Lie superalgebras. One is the standard approach, where a real form of a complex Lie superalgebra is a real Lie superalgebra such that its complexification is the original complex Lie superalgebra. The second is related to considering A-points of a Lie superalgebra over a commutative complex superalgebra A equipped with superconjugat...

Simple associative superalgebra with 2 independent supertraces is presented. Its commutant is a simple Lie superalgebra which has at least 2 independent invariant bilinear forms.

In this paper, the intuitionistic fuzzy Lie sub-superalgebras and ideals of Lie superalgebras are studied further. We define the intuitionistic fuzzy quotient Lie superalgebra by an intuitionistic fuzzy Lie ideal and prove that it is a Lie superalgebra. The intuitionistic fuzzy set of quotient Lie superalgebra is also considered. Finally, solvable intuitionistic fuzzy Lie ideals and nilpotent i...

We consider the supercircle S equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on S as the Lie superalgebra of contact vector fields; it contains the Möbius superalgebra osp(1|2). We study the space of linear differential operators on weighted densities as a module over osp(1|2). We introduce the canonical isomorphism between this space and the correspondin...