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

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.