Group algebra
In mathematics, the group algebra of a group G means, firstly, its group ring over a given field.It may mean also, in case G is a topological group, some other ring of functions on G, the group ring being the ring of functions with finite support. Suppose G is locally compact, so that Haar measure exists on G. The product in the group algebra will then always be of convolution type; and the values of functions considered will be complex numbers. In different contexts the condition imposed might be to have compact support; or to be integrable, giving rings Co(G) and L1(G), either of which can serve as a group algebra in the sense that representations of G become modules over that ring.
