In this paper, we shall classify “quadratic” conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra. Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.

Suppose that the underlying field is of characteristic different from 2 and 3. We first prove so-called stem deformations a free presentation finite-dimensional Lie superalgebra L exhaust all maximal extensions L, up to equivalence extensions. Then we multipliers covers always exist for they are unique isomorphisms. Finally, describe multipliers, covers, Heisenberg superalgebras model filiform ...

Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra based weight system. Le and Murakami showed that these two link invariants are the same. These constructions can be generalized to some classes of Lie super...

The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of for Yangian \( \mathrm{Y}(\mathfrak {gl}_{m|n})\) and use them to produce a transition rule parameters highest weight modules corresponding change parity sequence. This leads description finite-dimensional irreducible representations ...

We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN , BCN , BN , CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed — for arbitrary valu...

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...