We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

Making use of a Howe duality involving the infinite-dimensional Lie superalgebra ĝl∞|∞ and the finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of ĝl∞|∞ in terms of hook Schur functions. We use the reduction procedure of ĝl∞|∞ to ĝln|n to derive a character formula for a certain class of level 1 highest weight ir...

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...

The notions of N = 1 Neveu-Schwarz vertex operator superal-gebra over a Grassmann algebra and with odd formal variables and of N = 1 Neveu-Schwarz vertex operator superalgebra over a Grass-mann algebra and without odd formal variables are introduced, and we show that the respective categories of such objects are isomorphic. The weak supercommutativity and weak associativity properties for an N ...

The κ-deformedD = 4 Poincaré superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the κ-deformed D = 4 Poincaré superalgebra can be written as graded bicrossproduct. We show that the κ-deformed D = 4 superalgebra acts covariantly on κ-deformed chiral superspace. Institute of Physics, University of L...

In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...

Generalised scalar particle quantisation in 1 + 1 dimensions and D(2, 1; α) Abstract. The exceptional superalgebra D(2, 1; α) has been classified as a candidate conformal supersymmetry algera in two dimensions. We propose an alternative interpretation of it as an extended BFV-BRST quantisation superalgebra in 2D (D(2, 1; 1) ≃ osp(2, 2|2)). A superfield realization is presented wherein the stand...