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Representing Clifford algebras as crossed-products

✍ Scribed by Timothy J. Hodges; Steven B. Tesser

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
323 KB
Volume
123
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

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Let F be an arbitrary field and let D be a division algebra having center F which is finite dimensional over F. In general, there need not exist a maximal subfield E of D which is Galois over F. If such an E exists, we Ε½ call D a crossed product or G G-crossed product if G G is the Galois group of .

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We show that division algebras do not always embed in crossed product division algebras, so the latter do not serve as ''Galois closures'' for division algebras. We construct decomposable noncrossed product division algebras of prime-power index over rational function fields and Laurent series field