INVARIANTS OF 2 ORDER-3 SQUARE MATRICES

The invariants of a square matrix are all rational functions of coeffi cients of its characteristic polynomial. For several matrices, invaria nts of d square matrices of order n are known in few cases. They form the center Z(d,n) of the n(2)-dimensional division ring generated by d generic matrices over the field k. This field has the following prope rties: its transcendence degree is (d - )n(2) + 1 and it has a Galois extension, of Galois groupe S-n which is purely transcendental over k. The crucial case is d = 2 as Z(d,n) itself is purely transcendental o ver Z(2,n). Using Clifford algebras, we construct explicitly Z(2,3) an d we recover a result of E. Formanek.