WEBAug 22, 2024 · The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, hence of all elements of the form a_1g_1+a_2g_2+...+a_ng_n, (1) where a_i in K and g_i in G for all i=1,...,n.