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