The $\kappa$-Poincar\'e Group on a $C^*$-level

Abstract

The $C^*$-algebraic $\kappa$-Poincar\'{e} Group is constructed. The construction uses groupoid algebras of differential groupoids associated to Lie group decomposition. It turns out the underlying $C^*$-algebra is the same as for "$\kappa$-Euclidean Group" but a comultiplication is twisted by some unitary multiplier. Generators and commutation relations among them are presented.