We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every superalgebra $(V,\circ)$, we construct an enveloping differential Poisson $U(V)$ a derivation $d$ such that $u\circ v=ud(v)$ and ${u,v}=u\circ v-(-1)^{|u||v|}v\circ u$ for $u,v\in V$. The latter means the commutator Gelfand–Dorfman of $V$ is special. Next, prove constructed on finite-dimensional spec...

We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced function between the nonstandard hulls is smooth. We also discuss some conditions on...

We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily s...

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).

To a finite type knot invariant, weight system can be associated, which is function on chord diagrams satisfying so-called 4-term relations. In the opposite direction, each determines invariant. particular, associated to any metrized Lie algebra, and superalgebra. However, computation of these systems complicated. recent paper by present author, an extension gl(N)-weight arbitrary permutations ...

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...