Unitary SK1 of semiramified graded and valued division algebras

We prove formulas for SK 1 (E, τ ), which is the unitary SK 1 for a graded division algebra E finite-dimensional and semiramified over its center T with respect to a unitary involution τ on E. Every such formula yields a corresponding formula for SK 1 ( D , ρ ) where D is a division algebra tame and...

Full description

Saved in:
Bibliographic Details
Published in:Manuscripta mathematica 2012-11, Vol.139 (3-4), p.343-389
Main Author: Wadsworth, A. R.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove formulas for SK 1 (E, τ ), which is the unitary SK 1 for a graded division algebra E finite-dimensional and semiramified over its center T with respect to a unitary involution τ on E. Every such formula yields a corresponding formula for SK 1 ( D , ρ ) where D is a division algebra tame and semiramified over a Henselian valued field and ρ is a unitary involution on D . For example, it is shown that if where I 0 is a central simple T 0 -algebra split by N 0 and N is decomposably semiramified with with L 1 , L 2 fields each cyclic Galois over T 0 , then
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-011-0519-9