manuscripta mathematica

, Volume 109, Issue 4, pp 511–525

The hermitian level of composition algebras

  • S. Pumplün
  • T. Unger

DOI: 10.1007/s00229-002-0323-7

Cite this article as:
Pumplün, S. & Unger, T. Manuscripta Math. (2002) 109: 511. doi:10.1007/s00229-002-0323-7

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • S. Pumplün
    • 1
  • T. Unger
    • 2
  1. 1.Fakultät für Mathematik, Universität Regensburg, Universitätsstr. 31, D-93040 Regensburg, Germany. e-mail: susanne.pumpluen@mathematik.uni-regensburg.deDE
  2. 2.Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland. e-mail: thomas.unger@ucd.ieIE