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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Octonion planes over local rings

Author: Robert Bix
Journal: Trans. Amer. Math. Soc. 261 (1980), 417-438
MSC: Primary 17C40; Secondary 20H25
MathSciNet review: 580896
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Abstract: Let $ \mathcal{D}$ be an octonion algebra which is a free module over a local ring R and let $ J = H({\mathcal{D}_3},\gamma )$ be the quadratic Jordan algebra of Hermitian 3-by-3 matrices over R. We define the octonion plane determined by J and prove that every collineation is induced by a norm semisimilarity of J. We classify the subgroups of the collineation group normalized by the little projective group.

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Keywords: Octonion planes, exceptional Jordan algebras, norm semisimilarities, orthogonal groups over local rings
Article copyright: © Copyright 1980 American Mathematical Society

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