SK1 of graded division algebras
Identifieur interne : 000261 ( Main/Exploration ); précédent : 000260; suivant : 000262SK1 of graded division algebras
Auteurs : R. Hazrat [Royaume-Uni] ; A. R. Wadsworth [États-Unis]Source :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2011-06-01.
Abstract
Abstract: The reduced Whitehead group SK1 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 SK1 of a tame valued division algebra over a henselian field coincides with SK1 of its associated graded division algebra. Furthermore, it is shown that SK1 of a graded division algebra is isomorphic to SK1 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 SK1 for generic abelian crossed products.
Url:
DOI: 10.1007/s11856-011-0045-1
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001229
- to stream Istex, to step Curation: 001229
- to stream Istex, to step Checkpoint: 000222
- to stream Main, to step Merge: 000261
- to stream Main, to step Curation: 000261
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">SK1 of graded division algebras</title><author><name sortKey="Hazrat, R" sort="Hazrat, R" uniqKey="Hazrat R" first="R." last="Hazrat">R. Hazrat</name></author><author><name sortKey="Wadsworth, A R" sort="Wadsworth, A R" uniqKey="Wadsworth A" first="A. R." last="Wadsworth">A. R. Wadsworth</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:58B15825F7438F01CD67DBAA47961BD62DDCF118</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1007/s11856-011-0045-1</idno><idno type="url">https://api.istex.fr/document/58B15825F7438F01CD67DBAA47961BD62DDCF118/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001229</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001229</idno><idno type="wicri:Area/Istex/Curation">001229</idno><idno type="wicri:Area/Istex/Checkpoint">000222</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000222</idno><idno type="wicri:doubleKey">0021-2172:2011:Hazrat R:sk:of:graded</idno><idno type="wicri:Area/Main/Merge">000261</idno><idno type="wicri:Area/Main/Curation">000261</idno><idno type="wicri:Area/Main/Exploration">000261</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">SK1 of graded division algebras</title><author><name sortKey="Hazrat, R" sort="Hazrat, R" uniqKey="Hazrat R" first="R." last="Hazrat">R. Hazrat</name><affiliation wicri:level="1"><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>Department of Pure Mathematics, Queen’s University, BT7 1NN, Belfast</wicri:regionArea><wicri:noRegion>Belfast</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Royaume-Uni</country></affiliation></author><author><name sortKey="Wadsworth, A R" sort="Wadsworth, A R" uniqKey="Wadsworth A" first="A. R." last="Wadsworth">A. R. Wadsworth</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Mathematics, University of California at San Diego, 92093-0112, La Jolla, CA</wicri:regionArea><placeName><region type="state">Californie</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Israel Journal of Mathematics</title><title level="j" type="abbrev">Isr. J. Math.</title><idno type="ISSN">0021-2172</idno><idno type="eISSN">1565-8511</idno><imprint><publisher>The Hebrew University Magnes Press</publisher><pubPlace>Heidelberg</pubPlace><date type="published" when="2011-06-01">2011-06-01</date><biblScope unit="volume">183</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="117">117</biblScope><biblScope unit="page" to="163">163</biblScope></imprint><idno type="ISSN">0021-2172</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0021-2172</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The reduced Whitehead group SK1 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 SK1 of a tame valued division algebra over a henselian field coincides with SK1 of its associated graded division algebra. Furthermore, it is shown that SK1 of a graded division algebra is isomorphic to SK1 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 SK1 for generic abelian crossed products.</div></front></TEI><affiliations><list><country><li>Royaume-Uni</li><li>États-Unis</li></country><region><li>Californie</li></region></list><tree><country name="Royaume-Uni"><noRegion><name sortKey="Hazrat, R" sort="Hazrat, R" uniqKey="Hazrat R" first="R." last="Hazrat">R. Hazrat</name></noRegion><name sortKey="Hazrat, R" sort="Hazrat, R" uniqKey="Hazrat R" first="R." last="Hazrat">R. Hazrat</name></country><country name="États-Unis"><region name="Californie"><name sortKey="Wadsworth, A R" sort="Wadsworth, A R" uniqKey="Wadsworth A" first="A. R." last="Wadsworth">A. R. Wadsworth</name></region><name sortKey="Wadsworth, A R" sort="Wadsworth, A R" uniqKey="Wadsworth A" first="A. R." last="Wadsworth">A. R. Wadsworth</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000261 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000261 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:58B15825F7438F01CD67DBAA47961BD62DDCF118
|texte= SK1 of graded division algebras
}}
| This area was generated with Dilib version V0.6.33. |  |