A new construction of noncrossed product algebras

Jacob, Bill; Wadsworth, Adrian R.

doi:10.1090/S0002-9947-1986-0816320-X

A new construction of noncrossed product algebras
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by Bill Jacob and Adrian R. Wadsworth PDF

Trans. Amer. Math. Soc. 293 (1986), 693-721 Request permission

Abstract:

New examples of noncrossed product division algebras are obtained, using methods different from all previous noncrossed product constructions. The examples are division algebras over intersections of $p$-Henselian valued fields, and they have Schur index ${p^m}$ and exponent ${p^n}$ for any prime number $p$ and any integers $m \geqslant n \geqslant 2\;(n \geqslant 3\;{\text {if}}\;p = 2)$. The basic tools used in the construction are valuation theory and Galois cohomology; no generic methods are applied and there is no p.i. theory. Along the way, local-global principles are proved for central simple algebras over intersections of $p$-Henselian valued fields.

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