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...

We show that a set of monic polynomials in the free Lie superalgebra is a Gröbner-Shirshov basis for a Lie superalgebra if and only if it is a Gröbner-Shirshov basis for its universal enveloping algebra. We investigate the structure of GröbnerShirshov bases for Kac-Moody superalgebras and give explicit constructions of Gröbner-Shirshov bases for classical Lie superalgebras. Supported in part by...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

The second homology group H2(st(m,n,R)) of the Steinberg Lie superalgebra st(m,n,R)(m + n ≥ 5), which is trivial, has been studied by A.V.Mikhalev and I.A.Pinchuk in [MP]. In this paper, we will work out H2(st(m,n,R)) explicitly for m + n = 3, 4 which is also trivial when m + n = 3, but not necessarily trivial when m + n = 4. Introduction Steinberg Lie algebras stn(R) and/or their universal cov...

We determine the Lie superalgebras over fields of characteristic zero that are graded by the root system A(n, n) of the special linear Lie superalgebra psl(n + 1, n + 1).

There are well-known constructions of the exceptional simple Lie algebras of type E8 and F4 which go back to Witt [Wit41], as Z2-graded algebras g = g0̄⊕g1̄ with even part the orthogonal Lie algebras so16 and so9 respectively, and odd part given by their spin representations (see [Ada96]). Brown [Bro82] found a new simple finite dimensional Lie algebra over fields of characteristic 3 which presen...

1.1. In [PS1], I. Penkov and V. Serganova show that the category of representations of a basic classical Lie superalgebra g of type I with a fixed typical central character is equivalent to the category of representations of the even part g0 with a suitable central character. A similar result for type II was proven by I. Penkov in [P] for “generic” central characters. The aim of this paper is t...