Description
We present two distinct deformations of a given semisimple Lie group: the contraction onto the motion group, knwon as the Mackey-Higson deformation, and the quantisation of the symmetric pair related to a maximal compact subgroup, due to Letzter.
For low dimensional examples, we explain how to assemble these two deformations into a continuous field of C*-algebras defined over a square, which has vertically constant K-theory. We also show how the representation theory varies along this field in these cases.
