The hermitian level of composition algebras |
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| Authors: | S. Pumplün T. Unger |
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| Affiliation: | Fakult?t für Mathematik, Universit?t Regensburg, Universit?tsstr. 31, D-93040 Regensburg, Germany. e-mail: susanne.pumpluen@mathematik.uni-regensburg.de, DE
Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland. e-mail: thomas.unger@ucd.ie, IE
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| Abstract: | The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power of two when finite. Furthermore, any power of two can occur as the hermitian level of a composition algebra with non-standard involution. Some bounds are obtained for the hermitian level of a composition algebra with involution of the second kind. Received: 22 March 2002 / Revised version: 10 July 2002 Mathematics Subject Classification (2000): 17A75, 16W10, 11E25 |
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