Permutation Actions on Tensor Powers of the Quaternions
by
Finlay Thompson
Victoria University

The quaternions arise as the generator of the Brauer group of the reals. Using this basic fact it is possible to define an interesting finite group action on tensor powers of the algebra of quaternions by permuting the module structures.

These finite group actions have useful applications to tensor calculus on four manifolds. In particular we give some applications to study of non-flat local Lorentzian metrics.

Date received: October 18, 2000