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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Composition algebras over algebraic curves of genus zero


Author: Holger P. Petersson
Journal: Trans. Amer. Math. Soc. 337 (1993), 473-493
MSC: Primary 17A75; Secondary 14H99, 17A45, 17D05
MathSciNet review: 1108613
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Abstract: We rephrase the classical theory of composition algebras over fields, particularly the Cayley-Dickson Doubling Process and Zorn's Vector Matrices, in the setting of locally ringed spaces. Fixing an arbitrary base field, we use these constructions to classify composition algebras over (complete smooth) curves of genus zero. Applications are given to composition algebras over function fields of genus zero and polynomial rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1108613-X
PII: S 0002-9947(1993)1108613-X
Article copyright: © Copyright 1993 American Mathematical Society