Israel Journal of Mathematics

, Volume 183, Issue 1, pp 117–163 | Cite as

SK1 of graded division algebras

  • R. HazratEmail author
  • 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.


Abelian Group Exact Sequence Simple Root Division Algebra Division Ring 
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© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Department of Pure MathematicsQueen’s UniversityBelfastUK
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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