CHAIN EQUIVALENCE ON QUATERNIONS WITH TRIVIAL SUM

Abstract

We introduce a simple operation on isomorphism classes of n-tuples of quaternions with trivial sum in the Brauer group that corresponds to the notion of Witt's chain equivalence on quadratic forms. The aim of this note is to show that any two classes of n-tuples of quaternions with trivial sum are connected by an iterated application of such simple operations for all n <= 6. We also provide some applications to the norm residue homomorphism of degree 2 and to the R-triviality of the corresponding torsors.