it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

This text is an extended version of a part of my 1980 Trieste preprint [16]. In this preprint I gave, in particular, an expression for the action of a Lie superalgebra g on the g-module coinduced from an h-module V for the case where both g and V are finite-dimensional and g decomposes (as a linear space, not Lie superalgebra) into a direct sum g− ⊕ h with g− a Lie superalgebra. The importance ...

We classify anti-involutions of Lie superalgebra ŜD preserving the principal gradation, where ŜD is the central extension of the Lie superalgebra of differential operators on the super circle S. We clarify the relations between the corresponding subalgebras fixed by these anti-involutions and subalgebras of ĝl∞|∞ of types OSP and P . We obtain a criterion for an irreducible highest weight modul...

In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extensions of g⊗A where g is a basic classical Lie superalgebra and A is Laurent polynomial ring in several variables. The case where g is a simple finite dimensional Lie algebra is included.

Abstract. An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for so(n) and sp(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly o...

Recent work applying higher gauge theory to the superstring has indicated the presence of ‘higher symmetry’. Infinitesimally, this is realized by a ‘Lie 2-superalgebra’ extending the Poincaré superalgebra in precisely the dimensions where the classical superstring makes sense: 3, 4, 6 and 10. In the previous paper in this series, we constructed this Lie 2-superalgebra using the normed division ...

We analyse the Witten-Woronowicz's type deformations of the Lie su-peralgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite dimensional representations are formulated in terms of a finite difference operator, providing operators that are relevant for the classification of quasi exactly solvable, finite difference equations. Si...

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...

In this paper we use the Etingof-Kazhdan quantization of Lie bisuperalgebras to investigate some interesting questions related to DrinfeldJimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type superalgebra associated to a Lie superalgebra of type A-G, with the distinguished Cartan matrix, is isomorphic to the E-K quantization of the Lie s...