Aleksa Vujicic, University of Waterloo
The Spine of a Fourier Algebra
Given a locally compact group G, one can define the Fourier and Fourier-Stieltjes algebras A(G) and B(G), which in the abelian case, are isomorphic to L1(G^) and M(G^) respectively. The Fourier algebra A(G) is typically more tractable than B(G), and often easier to describe. A notable exception is when B(G) = A(G), which occurs precisely when G is compact.
The spine of a Fourier Algebra A*(G), introduced by M. Ilie and N. Spronk, is a subalgebra of B(G) which contains all A(H)∘η where η : G → H is a continuous homomorphism.
It has been shown that for G = Qp ⋊ Op*, that B(G) = A*(G), despite not being compact.
We also explore G = Qp^2 ⋊ Op*, where we have shown that although B(G) is strictly larger than A*(G), they are close to being similar.
MC 5417