SEMIPRIMITIVITY OF GROUP-ALGEBRAS OF INFINITE SIMPLE-GROUPS OF LIE TYPE

Let G be a simple group of Lie type over an infinite locally finite fi eld F. For any field K , we prove that the group algebra K[G] is semip rimitive. The argument here is a mixture of combinatorial and topologi cal methods. Combined with earlier results, it now follows that any gr oup algebra of an infinite locally finite simple group is semiprimitiv e. Furthermore, if the group is countably infinite, then the group alg ebra is primitive. In particular, if G is a simple group of Lie type o ver the field F, then K[G] is a primitive ring.