Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras

TL;DR

This paper introduces super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras, providing new construction methods, establishing their equivalence, and characterizing their central extensions, thus advancing the algebraic framework of superalgebras.

Contribution

It presents novel constructions, establishes the equivalence between quadratic Hom-Lie conformal superalgebras and super Hom-Gel'fand-Dorfman bialgebras, and characterizes their central extensions.

Findings

Constructed infinite-dimensional Hom-Lie superalgebras from super Hom-Gel'fand-Dorfman bialgebras.

Established a general method to construct Hom-Lie conformal superalgebras from Hom-Lie superalgebras.

Characterized one-dimensional central extensions using bilinear forms.

Abstract

The purpose of this paper is to introduce and study super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing super Hom-Gel'fand-Dorfman bialgebras and obtain some infinite-dimensional Hom-Lie superalgebras from affinization of super Hom-Gel'fand-Dorfman bialgebras. Also, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish equivalence of quadratic Hom-Lie conformal superalgebras and super Hom-Gel'fand-Dorfman bialgebras. Finally, we characterize one-dimensional central extensions of quadratic Hom-Lie conformal superalgebras by using certain bilinear forms of super Hom-Gel'fand-Dorfman bialgebras.