Homogeneous SK1 of simple graded algebras

摘要

For a simple graded algebra S=Mn(E) over a graded division algebra E, a short exact sequence is establishedrelating the reduced Whitehead group of the homogeneous part of S to that of E. In particular it is shown that the homogeneous SK1 is not in general Morita invariant. Along the way we prove the existence andmultiplicativity of a Dieudonné determinant for homogeneouselements of S.