ON THE TRIVIALITY OF CERTAIN WHITEHEAD GROUPS

Abstract

Let K be a field of arbitrary characteristic and let q be a prime number different from the characteristic of K. If A is a central simple algebra over whose index is a power of q, we show the triviality of the Whitehead groups SK₁ (A) and USK₁(A) when the cohomological q-dimension of 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 K₁Spin(A) are easily derived.