A characterization of the group algebras of the finite groups
Marc A. Rieffel · Pacific Journal of Mathematics · 1966
The following is proved: MAIN THEOREM.Let A be a finite dimensional Archemedian lattice ordered algebra which satisfies the following axioms: MO If f,g,he A, and if / ^ 0, then (1) Mgvh)= v{/i*flr+ /, 0, g > 0, then f*g > 0.Then there exists a finite group G such that A is order and algebra isomorphic to the group algebra of G.Some similar results are obtained for finite semigroups, and a few applications of these results are given.In particular it is shown that the second cohomology group, H 2 (S, R) 9 of any finite commutative semigroup, S, with coefficients in the additive group of real numbers, R, is trivial.