Lie Superalgebras arising from bosonic representation

TL;DR

This paper constructs a 2-toroidal Lie superalgebra using bosonic and ghost fields, revealing its structure as a central extension of a superalgebra with a distinguished subalgebra, and highlighting its similarities to known toroidal Lie superalgebras.

Contribution

It introduces a new construction of a 2-toroidal Lie superalgebra with explicit bosonic and ghost field representations, expanding the understanding of superalgebra structures.

Findings

The superalgebra contains $osp(1|2n)^{(1)}$ as a subalgebra.

It is a central extension of $osp(1|2n) imes ext{Laurent polynomials}$.

The algebra behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$.

Abstract

A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$. Furthermore this algebra is a central extension of the algebra $osp(1|2n)\otimes \mathbb C[s, s^{-1}, t,t^{-1}]$.