Patrick J. Morandi and S. Pumplün: On the tensor product of two composition algebras,

Submission: 1999, Nov. 5

In this paper we investigate the tensor product C of two composition algebras C1 and C2 over a field F. In the first part of the paper we use the Albert form of C, defined by B. Allison, to help determine the structure of C. In particular, we prove that the Witt index of the Albert form determines the maximal dimension of an algebra that is isomorphic to a subalgebra of both C1 and C2. In the second section we show that, if Ci is the Cayley-Dickson doubling of a quaternion algebra Qi, and if A is the tensor product of Q1 and Q2, then an F-algebra automorphism of C that stabilizes A is compatible with the standard tensor product involution on C, and so either stabilizes the Ci or interchanges them.

1991 Mathematics Subject Classification:

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