Fourier algebras of locally compact groups are important class of commutative Banach algebras containing much information on the underlying groups enough to distinguish them. However, extracting specific information on the group from the Fourier algebra is a highly nontrivial procedure in general. In this talk we will focus on the compact Lie group case and will discuss about how we can get the dimension information from the Banach algebraic property of the associated Fourier algebra. The key ingredient is making the Fourier algebra weighted. We will begin with the definition of Fourier algebras on compact groups and their weighted versions.
The talk is based on a joint work with M. Ghandehari/E. Samei/N. Spronk.