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Correspondences Between Valued Division Algebras and Graded Division Algebras
- Source :
- Journal of Algebra. 220(1):73-114
- Publication Year :
- 1999
- Publisher :
- Elsevier BV, 1999.
-
Abstract
- If D is a tame central division algebra over a Henselian valued field F, then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF. After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map [D] ↦ [GD]g yields an index-preserving isomorphism from the tame part of the Brauer group of F to the graded Brauer group of GF. This isomorphism is shown to be functorial with respect to field extensions and corestrictions, and using this it is shown that there is a correspondence between F-subalgebras of D (with center tame over F) and graded GF-subalgebras of GD.
- Subjects :
- Discrete mathematics
Pure mathematics
Algebra and Number Theory
Mathematics::Commutative Algebra
Mathematics::Rings and Algebras
Graded ring
Graded Lie algebra
Field extension
Mathematics::K-Theory and Homology
Differential graded algebra
Division ring
Division algebra
Central simple algebra
Mathematics::Representation Theory
Brauer group
Mathematics
Subjects
Details
- ISSN :
- 00218693
- Volume :
- 220
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi.dedup.....635f1fe6dea596aac687b75c9df8ff68
- Full Text :
- https://doi.org/10.1006/jabr.1999.7903