|Date||Oct 10, 2018|
Fourier algebras are preduals of group von Neumann algebras, whose Banach algebra structure contain all the information on the underlying locally compact group. For example, its Gelfand spectrum allows us to recover the topological structure of the underlying group. In this talk we will introduce a weighted version of Fourier algebras with the hope to obtain a different aspects of underlying groups through Gelfand spectra. It turns out that we can actually "detect" complexification structure when the group is a Lie group. We will cover the details of easily accessible cases, namely the case of compact Lie groups with the necessary preliminaries including some Lie theory terminologies in the first seminar. Among compact Lie groups we will examine the case of SU(n) in detail. At the end of the seminar we will address the technicality of defining the weighted Fourier algebra of general locally compact groups.