SOLVABLE CROSSED PRODUCT ALGEBRAS REVISITED

BROWN, CHRISTIAN ; PUMPLÜN, SUSANNE 

Glasgow mathematical journal, Tome 62 (2020), pp. S165-S185

Résumé

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.

Détail

DOI : 10.1017/S0017089519000089

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