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V.—On Certain Classes of Linear Algebras of Genus One

Published online by Cambridge University Press:  14 February 2012

E. M. Patterson
E. M. Patterson
Affiliation:
University of Leeds
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Synopsis

A result proved elsewhere concerning the structure of linear algebras of genus one is used (i) to classify Jordan algebras of genus one, and (ii) to obtain necessary and sufficient conditions for an algebra of genus one to be simple. The class of simple Jordan algebras of genus one and dimension not less than 4 over an algebraically closed field is shown to coincide with the class of simple Jordan algebras of degree two.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 1 , 1958 , pp. 63 - 71
Copyright
Copyright © Royal Society of Edinburgh 1958

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References

References to Literature

Albert, A. A., 1944. “Two element generation of a separable algebra”, Bull. Amer. Math. Soc., 50, 786–788.CrossRefGoogle Scholar
Albert, A. A., 1947. “A structure theory for Jordan algebras”, Ann. Math., Princeton, 48, 546–567.CrossRefGoogle Scholar
Knebelman, M. S., 1935. “Classification of Lie algebras”, Ann. Math., Princeton, 36, 46–56.CrossRefGoogle Scholar
Kuranishi, M., 1952. “On everywhere dense imbeddings of free groups in Lie groups”, Nagoya Math. J., 2, 63–71.CrossRefGoogle Scholar
Patterson, E. M., 1956. “Linear algebras of genus zero”, J. Lond. Math. Soc., 31, 326–331.CrossRefGoogle Scholar
Patterson, E. M., 1957 a. “Linear algebras of genus one admitting a unit element”, J. Lond. Math. Soc., 32, 88–94.CrossRefGoogle Scholar
Patterson, E. M., 1957 b. “Generators of linear algebras”, Proc Lond. Math. Soc., 7, 467–480.CrossRefGoogle Scholar
Wallace, E. W., 1956. “On the classification of Lie algebras”, Thesis, University of Liverpool, 1956.Google Scholar