New York Journal of Mathematics
Volume 18 (2012) 315-336

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R. Hazrat and A. R. Wadsworth

Homogeneous SK1 of simple graded algebras

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Published: May 10, 2012
Keywords: Reduced Whitehead group, Graded division algebras, Dieudonné determinant
Subject: 16W60, 19B99 (primary), 16K20 (secondary)
Abstract
For a simple graded algebra S=Mn(E) over a graded division algebra E, a short exact sequence is established relating the reduced Whitehead group of the homogeneous part of S to that of E. In particular it is shown that the homogeneous SK1 is not in general Morita invariant. Along the way we prove the existence and multiplicativity of a Dieudonné determinant for homogeneous elements of S.
Acknowledgements

This work was supported by the Engineering and Physical Sciences Research Council [grant EP/I007784/1]
Author information

R. Hazrat:
Department of Pure Maths., Queen's University, Belfast BT7 1NN, United Kingdom,
School of Computing, Engineering and Mathematics, University of Western Sydney, Australia
r.hazrat@uws.edu.au

A. R. Wadsworth:
Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112, U.S.A.
arwadsworth@ucsd.edu