Models of the exceptional simple modular Lie superalgebras in characteristic p ≥ 3, that have appeared in the classification due to Bouarroudj, Grozman and Leites [BGLb] of the Lie superalgebras with indecomposable symmetrizable Cartan matrices, are provided. The models relate these exceptional Lie superalgebras to some low dimensional nonassociative algebraic systems. Introduction The finite d...

The issue of constructing N=1,2,3 supersymmetric extensions the l-conformal Galilei algebra is reconsidered following approach in [JHEP 1709 (2017) 131]. Drawing a parallel between acceleration generators entering superalgebra and irreducible supermultiplets d=1, N-extended superconformal group, new N=1 superalgebra, two N=2 variants, N=3 versions are built. Realisations terms differential oper...

We introduce the notion of a Lie-like algebra⋄ (superalgebra⋄) for ⋄ ∈ { , , 3−rd }. By bundling a family of algebras, we introduce six new generalizations of Lie algebras which are called Lie-like algebras or Lie-like superalgebras in this paper. The examples of the new generalizations of Lie algebras come from an invariant algebra (or an invariant superalgebra), where the notion of an invaria...

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...

Linear operators preserving the direct sum of polynomial rings P(m)⊕P(n) are constructed. In the case |m − n| = 1 they correspond to atypical representations of the superalgebra osp(2,2). For |m − n| = 2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed. PACS numbers: 02.20.Sv, 03.65.Fd ...

We present a new supersymmetric integrable model: the N = 2 superconformal affine Liouville theory. It interpolates between the N = 2 super Liouville and N = 2 super sineGordon theories and possesses a Lax representation on the complex affine Kac-Moody superalgebra ˆ sl(2|2)(1). We show that the higher spin W1+∞-type symmetry algebra of ordinary conformal affine Liouville theory extends to a N ...

Representations of the superalgebra osp(2|2) and current superalgebra osp(2|2) (1) k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2|2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2|2) (1) k in the standard basis are obtained for arbitrary level k.

It is known that the M2-brane worldvolume superalgebra includes two p-form central charges that encode the M-theory intersections involving M2-branes. In this paper we show by explicit computation that the Bagger-Lambert Lagrangian realizes the M2-brane superalgebra, including also the central extensions. Solitons of the Bagger-Lambert theory, that are interpreted as worldvolume realizations of...

A representation of the quantum superalgebra Uq(sl(M + 1|N + 1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag manifold. This realization provides us with a guide to construct the free field realization for the quantum affine superalgebra Uq(ŝl(M + 1|N + 1)) at arbitrary...

In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2, 1; ε), which recovers su(2|2) when the parameter ε is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and...