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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0580896-5
PII: S 0002-9947(1980)0580896-5
Keywords: Octonion planes, exceptional Jordan algebras, norm semisimilarities, orthogonal groups over local rings
Article copyright: © Copyright 1980 American Mathematical Society