Involutions on composition algebras

2005

Proc. Amer. Math. Soc.

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“…Conversely, we know that τ • = • τ , for any involution τ on C [Pu1]. Hence t τ (x) = τ (x)x +xτ (x).…”

Section: Proposition (I) Let a Be Any R-algebra With A Scalar Involumentioning

confidence: 98%

Sums of squares in octonion algebras

2005

Proc. Amer. Math. Soc.

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“…Moreover, if is a quaternion algebra over X with a noncanonical involution of the first kind, then Cay N and u v = ū v is the hatinvolution on [19].…”

Section: Involutions On Quaternion Algebrasmentioning

confidence: 99%

A Construction Method for Albert Algebras over Algebraic Varieties

Communications in Algebra

2015

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The hermitian level of composition algebras

manuscripta mathematica

Unger

2002

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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 nonstandard involution. Some bounds are obtained for the hermitian level of a composition algebra with involution of the second kind.