Many work was done for filiform Lie algebras defined by M. Vergne [8]. An interesting fact is that this algebras are obtained by deformations of the filiform Lie algebra Ln,m. This was used for classifications in [4]. Like filiform Lie algebras, filiform Lie superalgebras are obtained by nilpotent deformations of the Lie superalgebra Ln,m. In this paper, we recall this fact and we study even co...

A superconformal algebra is a simple complex Lie superalgebra g spanned by the coefficients of a finite family of pairwise local fields a(z) = ∑ n∈Z a(n)z , one of which is the Virasoro field L(z), [3, 8, 11]. Superconformal algebras play an important role in the string theory and conformal field theory. The Lie superalgebras K(N) of contact vector fields with Laurent polynomials as coefficient...

Inequivalent N = 2 supersymmetrizations of the `-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the N = 2 supersymmetry. For non-negative integer and half-integer ` both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N = 2 case coincides with the supera...

Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an element of this superalgebra which turns out to be a dynamical superalgebra for this system. The supercoherent states, defined by means of a supergroup displacemen...

Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...

Let e be an arbitrary even nilpotent element in the general linear Lie superalgebra glM|N and let We associated finite W-superalgebra. Ym|n super Yangian to glm|n. A subalgebra of Ym|n, called shifted denoted by Ym|n(σ), is defined studied. Moreover, explicit isomorphism between a quotient Ym|n(σ) established.