On the C*-Algebras Generated By the Quasi-Regular Representation of Locally Compact Group

In this paper, we investigate the structure of the quasi-regular representation of locally compact groups, particularly focusing on the amenability of the homogeneous factorspace G=H by analyzing the C*-algebras generated by the left quasi-regular representation λG=H. Our main result extends Theorem ۱ in [۱], establishing a connection between the amenability of the homogeneous space G=H and the existence of a nonzero multiplicative linear functional on C*(λG=H (G)).

Keywords:

Left quasi-regular representation , group C*−algebras , amenability , Homogeneous factor space