A Weak Hasse Principle for Central Simple Algebras with an Involution

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Date
2001
Authors
Lewis, David W.
Unger, Thomas
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Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001 / Hoffman, J. William et al. (ed.). - Bielefeld, 2001. - (Documenta mathematica ; 2001,1). - pp. 241-251
Abstract
The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generalizes a known result from quadratic form theory.
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Subject (DDC)
510 Mathematics
Keywords
Real fields,central simple algebras,involutions,weak Hasse principles,hermitian squares
Conference
Quadratic Forms and Related Topics, Mar 26, 2001 - Mar 30, 2001, Baton Rouge, Louisiana, USA
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Cite This
ISO 690LEWIS, David W., Claus SCHEIDERER, Thomas UNGER, 2001. A Weak Hasse Principle for Central Simple Algebras with an Involution. Quadratic Forms and Related Topics. Baton Rouge, Louisiana, USA, Mar 26, 2001 - Mar 30, 2001. In: HOFFMAN, J. William, ed. and others. Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001. Bielefeld, pp. 241-251
BibTex
@inproceedings{Lewis2001Hasse-23583,
  year={2001},
  title={A Weak Hasse Principle for Central Simple Algebras with an Involution},
  number={2001,1},
  address={Bielefeld},
  series={Documenta mathematica},
  booktitle={Proceedings of the Conference on Quadratic Forms and Related Topics : Baton Rouge, Louisiana, USA ; March 26 - 30, 2001},
  pages={241--251},
  editor={Hoffman, J. William},
  author={Lewis, David W. and Scheiderer, Claus and Unger, Thomas}
}
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