Cyclic homology of Jordan superalgebras and related Lie superalgebras

TL;DR

This paper explores the connection between cyclic homology of Jordan superalgebras and the second cohomology of their associated Lie superalgebras, with applications to Hamiltonian and contact Lie superalgebras.

Contribution

It establishes a relationship between cyclic homology and second cohomology for Jordan superalgebras, extending to specific classes like Hamiltonian and contact superalgebras.

Findings

Computed second cohomologies of specific Lie superalgebras

Established links between cyclic homology and cohomology in superalgebra context

Provided universal central extensions for Hamiltonian and contact superalgebras

Abstract

We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras. The obtained results are applied to computation of second cohomologies and universal central extensions of Hamiltonian and contact type Lie superalgebras over arbitrary rings of coefficients.