Deformed and extended Galilei group Hopf algebras

Abstract

The $\hat\kappa$-deformed extended Galilei Hopf group algebra, ${\rm Fun}_{\hat\kappa}(\tilde G_{(m)})$, is introduced. It provides an example of a cocycle bicrossproduct structure, and is shown to be the contraction limit of a pseudoextension of the $\kappa$-Poincar\'e group algebra. The possibility of obtaining another deformed extended Galilei groups is discussed, including one obtained from a non-standard Poincar\'e deformation.