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The hermitian level of composition algebras

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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.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Regensburg, Universitätsstr. 31, D-93040 Regensburg, Germany. e-mail: susanne.pumpluen@mathematik.uni-regensburg.de, , , , , , DE

    S. Pumplün

  2. Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland. e-mail: thomas.unger@ucd.ie, , , , , , IE

    T. Unger

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  1. S. Pumplün
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  2. T. Unger
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Received: 22 March 2002 / Revised version: 10 July 2002

Mathematics Subject Classification (2000): 17A75, 16W10, 11E25

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Pumplün, S., Unger, T. The hermitian level of composition algebras. Manuscripta Math. 109, 511–525 (2002). https://doi.org/10.1007/s00229-002-0323-7

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  • DOI: https://doi.org/10.1007/s00229-002-0323-7

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