In his classification of irreducible characters of a finite group of Lie type, Lusztig developes a theory in which a so-called non abelian Fourier transform emerges. This is a matrix which only depends on the Weyl group of the group of Lie type. Geck and Malle set up a system of axioms based on the properties such a Fourier matrix has. Using this system Brou\'e, Malle and Michel construct analogous transformations for the spetses, which until now remain mysterious objects. These transformations correspond to certain algebras which essentially have the properties of table algebras. In this talk, we will look at some results about the structure of these algebras.