Boosts superalgebras based on centrally-extended su(1|1)^2

TL;DR

This paper explores the structure of boost operators within centrally-extended su(1|1)^2 superalgebras, classifying their interactions and constructing coproduct maps to understand their algebraic relationships.

Contribution

It introduces a classification of superalgebras with boost operators based on their interactions and provides explicit coproduct constructions.

Findings

Identified a family of superalgebras with boost operators

Classified interactions between two su(1|1)^2 copies

Constructed coproduct maps for each algebra

Abstract

In this paper, we studied the boost operator in the setting of su(1|1)^2. We find a family of different algebras where such an operator can consistently appear, which we classify according to how the two copies of the su(1|1)^2 interact with each other. Finally, we construct coproduct maps for each of these algebras and discuss the algebraic relationships among them.