We prove that δ-derivations of a simple finite-dimensional Lie algebra over field characteristic zero, with values in module, are either inner derivations, or, the case adjoint multiplications by scalar, or some exceptional cases related to sl(2). This can be viewed as an extension classical first Whitehead Lemma.

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 describe the centre of a simple Lie superalgebra of type P (n). The description is based on the notion of anticentre.

We show that the 1 + 1-dimensional quantum superplane introduced by Manin is a quantum supergroup according to the Faddeev-Reshetikhin-Takhtajan approach. We give its supermatrix element, its corresponding R-matrix and its Hopf structure. This new point of view allows us, first, to realize its dual Hopf superalgebra starting from postulated initial pairings. Second, we construct a right-invaria...

Superimposed D–branes have matrix–valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativi...

There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct characters on Λ and eight distinct families of weight functions on chord diagrams. As a consequence we ...

A possible notion of superspace associated to a given 3-dimensional Lie algebra g0 might be a Lie superalgebra g g0 ⊕ g1. If one is to introduce a minimal set of assumptions, it seems quite natural to consider those superalgebras for which g1 g0 and for which the g0 action on g1 is the adjoint representation. A complete classification of the real and complex 3, 3 -dimensional Lie superalgebras ...

We say that a Lie (super)algebra is ''symmetric'' if with every root (with respect to the maximal torus) it has opposite of same multiplicity. Over algebraically closed fields positive characteristics (up 7 or 11, enough formulate general conjecture), we computed cohomology corresponding infinitesimal deformations all known simple finite-dimensional symmetric (super)algebras rank $<9$, except f...

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...

We study the representation theory of the superconformal algebra Wk(g, fθ) associated to a minimal gradation of g. Here, g is a simple finite-dimensional Lie superalgebra with a non-degenerate even supersymmetric invariant bilinear form. Thus, Wk(g, fθ) can be the Virasoro algebra, the Bershadsky-Polyakov algebra, the Neveu-Schwarz algebra, the BershadskyKnizhnik algebras, the N = 2 superconfor...