Koecher’s principle for quadratic Jordan algebras
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- by Kevin McCrimmon
- Proc. Amer. Math. Soc. 28 (1971), 39-43
- DOI: https://doi.org/10.1090/S0002-9939-1971-0299649-0
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Abstract:
In this note we indicate two techniques for establishing identities in quadratic Jordan algebras. The first method, due to Professor M. Koecher, shows that to establish an identity in general it suffices to establish it when all the elements involved are invertible. The second technique involves interpreting a given identity in a Jordan algebra as a simpler identity in a homotope of that algebra. These two techniques are applied to derive some important identities.References
- John R. Faulkner, The inner derivations of a Jordan algebra, Bull. Amer. Math. Soc. 73 (1967), 208–210. MR 212062, DOI 10.1090/S0002-9904-1967-11682-3
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099, DOI 10.1090/coll/039
- Kevin McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1072–1079. MR 202783, DOI 10.1073/pnas.56.4.1072
- Robert E. Lewand and Kevin McCrimmon, Macdonald’s theorem for quadratic Jordan algebras, Pacific J. Math. 35 (1970), 681–706. MR 299648, DOI 10.2140/pjm.1970.35.681
- Kevin McCrimmon, A characterization of the radical of a Jordan algebra, J. Algebra 18 (1971), 103–111. MR 277583, DOI 10.1016/0021-8693(71)90129-3
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 39-43
- MSC: Primary 17C05
- DOI: https://doi.org/10.1090/S0002-9939-1971-0299649-0
- MathSciNet review: 0299649