On the decomposition of cyclic algebras
Identifieur interne : 001109 ( Main/Exploration ); précédent : 001108; suivant : 001110On the decomposition of cyclic algebras
Auteurs : H. Rowen [Israël] ; -P. Tignol [Belgique]Source :
- Israel Journal of Mathematics [ 0021-2172 ] ; 1996-06-01.
Abstract
Abstract: A cyclic algebra (K/F, σ, a) of degreen hasproperty D(f) if it decomposes as a tensor product of a cyclic algebra of degreee=n/f containingL (the fixed subfield underσ e) and a cyclic subalgebra of degreef containing af-th root ofa. AlthoughD(2) holds for every cyclic algebra of degree 4 and exponent 2,D(p) fails for Brauer algebras of degreep 2 and exponentp, andD(2) fails for Brauer algebras of degree 8 and exponent 2. Using this, one fills the gap in [6, Theorem 4] and [7, Theorem 7.3.28], to show that the example given there is indeed tensor indecomposable of degreep 2 and exponentp. An easy ultraproduct argument provides an example containing allp k roots of 1, for allk.
Url:
DOI: 10.1007/BF02937323
Affiliations:
- Belgique, Israël
- Province du Brabant wallon, Région wallonne
- Louvain-la-Neuve
- Université catholique de Louvain
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Rowen</name><affiliation wicri:level="1"><country xml:lang="fr">Israël</country><wicri:regionArea>Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan</wicri:regionArea><wicri:noRegion>Ramat-Gan</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Israël</country></affiliation></author><author><name sortKey="Tignol, P" sort="Tignol, P" uniqKey="Tignol " first="-P." last="Tignol">-P. Tignol</name><affiliation wicri:level="4"><country xml:lang="fr">Belgique</country><wicri:regionArea>Département de Mathématiques, Université catholique de Louvain, B-1348, Louvain-la-Neuve</wicri:regionArea><orgName type="university">Université catholique de Louvain</orgName><placeName><settlement type="city">Louvain-la-Neuve</settlement><region type="region" nuts="1">Région wallonne</region><region type="province" nuts="1">Province du Brabant wallon</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Belgique</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Israel Journal of Mathematics</title><title level="j" type="abbrev">Israel J. Math.</title><idno type="ISSN">0021-2172</idno><idno type="eISSN">1565-8511</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-06-01">1996-06-01</date><biblScope unit="volume">96</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="553">553</biblScope><biblScope unit="page" to="578">578</biblScope></imprint><idno type="ISSN">0021-2172</idno></series><idno type="istex">923EB0F2B0AE11E4700A608E96E9AD7D8BD945AE</idno><idno type="DOI">10.1007/BF02937323</idno><idno type="ArticleID">Art15</idno><idno type="ArticleID">BF02937323</idno></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: A cyclic algebra (K/F, σ, a) of degreen hasproperty D(f) if it decomposes as a tensor product of a cyclic algebra of degreee=n/f containingL (the fixed subfield underσ e) and a cyclic subalgebra of degreef containing af-th root ofa. AlthoughD(2) holds for every cyclic algebra of degree 4 and exponent 2,D(p) fails for Brauer algebras of degreep 2 and exponentp, andD(2) fails for Brauer algebras of degree 8 and exponent 2. Using this, one fills the gap in [6, Theorem 4] and [7, Theorem 7.3.28], to show that the example given there is indeed tensor indecomposable of degreep 2 and exponentp. An easy ultraproduct argument provides an example containing allp k roots of 1, for allk.</div></front></TEI><affiliations><list><country><li>Belgique</li><li>Israël</li></country><region><li>Province du Brabant wallon</li><li>Région wallonne</li></region><settlement><li>Louvain-la-Neuve</li></settlement><orgName><li>Université catholique de Louvain</li></orgName></list><tree><country name="Israël"><noRegion><name sortKey="Rowen, H" sort="Rowen, H" uniqKey="Rowen H" first="H." last="Rowen">H. Rowen</name></noRegion><name sortKey="Rowen, H" sort="Rowen, H" uniqKey="Rowen H" first="H." last="Rowen">H. Rowen</name></country><country name="Belgique"><region name="Région wallonne"><name sortKey="Tignol, P" sort="Tignol, P" uniqKey="Tignol " first="-P." last="Tignol">-P. Tignol</name></region><name sortKey="Tignol, P" sort="Tignol, P" uniqKey="Tignol " first="-P." last="Tignol">-P. Tignol</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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