The $\kappa$-Poincaré Group on a $C^{\ast }$-level

Abstract

The $C^{\ast }$-algebraic $\kappa$-Poincaré Group is constructed. The construction uses groupoid algebras of differential groupoids associated to Lie group decomposition. It turns out the underlying $C^{\ast }$-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.

33 pages, no figures