### SK1 of graded division algebras, by R. Hazrat and A. R. Wadsworth

The reduced Whitehead group SK1 of a graded division algebra graded by a
torsion-free abelian group is studied. It is observed that the computations
here are much more straightforward than in the non-graded setting. Bridges to
the ungraded case are then established by the following two theorems: It is
proved that SK1 of a tame valued division algebra over a henselian field
coincides with SK1 of its associated graded division algebra. Furthermore, it
is shown that SK1 of a graded division algebra is isomorphic to SK1 of its
quotient division algebra. The first theorem gives the established formulas for
the reduced Whitehead group of certain valued division algebras in a unified
manner, whereas the latter theorem covers the stability of reduced Whitehead
groups, and also describes SK1 for generic abelian crossed products.

R. Hazrat <r.hazrat@qub.ac.uk,>

A. R. Wadsworth <wadswrth@math.ucsd.edu>