SK1-like functors for division algebras

Roozbeh Hazrat

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

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 SK1. 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 SK1(D). As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.
Original languageEnglish
Pages (from-to)573-588
Number of pages16
JournalJournal of Algebra
Volume239(2)
Issue number2
DOIs
Publication statusPublished - 15 May 2001

ASJC Scopus subject areas

  • Algebra and Number Theory

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