ON THE TRIVIALITY OF CERTAIN WHITEHEAD GROUPS

Abstract

Let Κ be a field of arbitrary characteristic and let g be a prime number different from the characteristic of K. If A is a central simple algebra over Κ whose index is a power of q, we show the triviality of the Whitehead groups SKi(A) and USKi(A) when the cohomological ^-dimension of Κ is at most 2. We give a global version of this result and indicate what can be done in the case where the index of the algebra is a power of the characteristic of the field. Triviality results of the Whitehead group KiSpin(A) are easily derived.