SK1-like functors for division algebras


Autoria(s): Hazrat, Roozbeh
Data(s)

15/05/2001

Resumo

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.

Identificador

http://pure.qub.ac.uk/portal/en/publications/sk1like-functors-for-division-algebras(083977d3-1bc7-4fb7-a089-77711c5fc8cf).html

http://dx.doi.org/10.1006/jabr.2000.8708

http://www.scopus.com/inward/record.url?scp=0035874250&partnerID=8YFLogxK

Idioma(s)

eng

Direitos

info:eu-repo/semantics/restrictedAccess

Fonte

Hazrat , R 2001 , ' SK1-like functors for division algebras ' Journal of Algebra , vol 239(2) , no. 2 , pp. 573-588 . DOI: 10.1006/jabr.2000.8708

Palavras-Chave #/dk/atira/pure/subjectarea/asjc/2600/2602 #Algebra and Number Theory
Tipo

article