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Solvable crossed product algebras revisited

Brown, Christian; Pumpluen, Susanne

Solvable crossed product algebras revisited Thumbnail


Authors

Christian Brown



Abstract

For any central simple algebra over a field F which contains a maximal subfield M with non-trivial automorphism group G = AutF (M), G is solvable if and only if the algebra contains a finite chain of subalgebras which are generalized cyclic algebras over their centers (field extensions of F) satisfying certain conditions. These subalgebras are related to a normal subseries of G. A crossed product algebra F is hence solvable if and only if it can be constructed out of such a finite chain of subalgebras. This result was stated for division crossed product algebras by Petit, and overlaps with a similar result by Albert which, however, was not explicitly stated in these terms. In particular, every solvable crossed product division algebra is a generalized cyclic algebra over F .

Citation

Brown, C., & Pumpluen, S. (2019). Solvable crossed product algebras revisited. Glasgow Mathematical Journal, 1-21. https://doi.org/10.1017/S0017089519000089

Journal Article Type Article
Conference Name Workshop on Nonassociative Algebra and Applications
Start Date Jul 9, 2018
End Date Jul 13, 2018
Acceptance Date Feb 13, 2019
Online Publication Date Apr 8, 2019
Publication Date Apr 8, 2019
Deposit Date Apr 8, 2019
Publicly Available Date Oct 9, 2019
Journal Glasgow Mathematical Journal
Print ISSN 0017-0895
Electronic ISSN 1469-509X
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Pages 1-21
DOI https://doi.org/10.1017/S0017089519000089
Keywords General Mathematics
Public URL https://nottingham-repository.worktribe.com/output/1562901
Publisher URL https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/solvable-crossed-product-algebras-revisited/C3E1991F0D9B3738FA311C274CC3EF5B
Related Public URLs https://arxiv.org/abs/1702.04605

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