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SK1-like Functors for Division Algebras

✍ Scribed by R Hazrat

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
146 KB
Volume
239
Category
Article
ISSN
0021-8693

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✦ Synopsis

We investigate the group valued functor G D = D * /F * D where D is a division algebra with center F and D the commutator subgroup of D * . We show that G has the most important functorial properties of the reduced Whitehead group SK 1 . We then establish a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra. The structure of G D turns out to carry significant information about the arithmetic of D. Along these lines, we employ G D to compute the group SK 1 D . As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.

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