We classify irreducible representations of finite W-algebra for the queer Lie superalgebra Q(n) associated with principal nilpotent coadjoint orbits. use this classification and our previous results to obtain a finite-dimensional super Yangian YQ(1).

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3, 6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3) × sl(2) × gl(1) as the zero degree component of its consistent Z-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3, 6), completi...

This work is devoted to the study of central extensions some solvable Leibniz superalgebras. We show that a superalgebra with non-null center can be obtained by extension other ones lower dimensions. Moreover, we describe for maximal Lie superalgebras nilradical which neither characteristically nilpotent in non-split case nor do not involve as term split case. Additionally, apply two different ...

Abstract All results concern characteristic 2. We describe two procedures; each of which to every simple Lie algebra assigns a superalgebra. prove that finite-dimensional superalgebra is obtained as the result one these procedures. For algebras, in addition known “classical” restrictedness, we introduce (2,4)-structure on non-alternating series: orthogonal and Hamiltonian vector fields. superal...

0.1. Let g be a complex finite-dimensional contragredient Lie superalgebra. These algebras were classified by V. Kac in [K1] and the list (excluding Lie algebras) consists of four series: A(m|n), B(m|n), C(m), D(m|n) and the exceptional algebrasD(2, 1, a), F (4), G(3). The finite-dimensional contragredient Lie superalgebras with zero Killing form (or, equivalently, with dual Coxeter number equa...

We describe transposed Poisson algebra structures on Block Lie algebras B(q) and superalgebras S(q), where q is an arbitrary complex number. Specifically, we show that the are trivial whenever q∉Z, for each q∈Z there only one (up to isomorphism) non-trivial structure B(q). The superalgebra S(q) admits q≠0 two non-isomorphic q=0. As a consequence, new admit Hom-Lie found.

In the present paper, we study notion of Schur multiplier M(L) an n-Lie superalgebra L=L0?L1 and prove that dim M(L)??i=0n(mi)L(n?i,k), where L0=m, L1=k, L(0,k)=1 L(t,k)=?j=1t(t?1j?1)(kj), for 1?t?n. Moreover, obtain upper bound dimension in which L is a nilpotent with one-dimensional derived superalgebra. It also provided several inequalities on as well analogue converse Schur’s theorem.

Generalized quantum statistics (GQS) associated to a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie superalgebras. In the current paper we finalize this classification for all exceptional Lie algebras and superalgebras. Since the definition of GQS is closely rel...

We establish that for the type I Lie superalgebras $sl(m/n)$ and $osp(2/2n)$, each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from explicit evaluation $H^1$ superalgebra cohomology valued in tensor product its dual.