SK1 for graded division algebras
| dc.creator | Hazrat, R. | |
| dc.creator | Wadsworth, A. R. | |
| dc.date | 2008-12-17 | |
| dc.date.accessioned | 2026-07-07T12:20:14Z | |
| dc.date.available | 2026-07-07T12:20:14Z | |
| dc.description | The reduced Whitehead group $\SK$ 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 $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ 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 $\SK$ for generic abelian crossed products. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/0812.3433 | |
| dc.identifier | http://arxiv.org/abs/0812.3433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213008 | |
| dc.subject | Rings and Algebras | |
| dc.title | SK1 for graded division algebras | |
| dc.type | text |