Poisson and Hopf structures for finite groups via star product and convolution

Abstract

A geometric approach is employed to introduce a nontrivial Poisson bracket for the function space L² (G) of a nite group G. This allows a tensor formulation of a known family of noncommutative star products ^⋆λ0 and the usual convolution product ∗c. Hopf structures for the same space are derived from matricial elements of irreducible representations.