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Mal'cev H*-algebras

Published online by Cambridge University Press:  24 October 2008

M. Cabrera-Garcia ,
J. Martinez-Moreno  and
A. Rodriguez-Palacios
M. Cabrera-Garcia
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071-Granada, Spain
J. Martinez-Moreno
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071-Granada, Spain
A. Rodriguez-Palacios
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071-Granada, Spain
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Abstract

The only finite-dimensional simple non-Lie Mal'cev complex algebra is given the structure of an H*-algebra and it is proved that this is the only topologically simple non-Lie Mal'cev H*-algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 463 - 471
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Ambrose, W.. Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364–386.CrossRefGoogle Scholar
[2]Bonsall, F. F. and Duncan, J.. Complete Normed Algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
[3]Braun, H. and Koecher, M.. Jordan-Algebren (Springer-Verlag, 1966).Google Scholar
[4]Cuenca, J. A. and Rodriguez, A.. Isomorphisms of H *-algebras. Math. Proc. Cambridge Philos. Soc. 97 (1985), 93–99.Google Scholar
[5]Cuenca, J. A. and Rodriguez, A.. Structure theory for noncommutative Jordan H *-algebras. J. Algebra 106 (1987), 1–14.Google Scholar
[6]Kleinfeld, E.. Simple alternative rings. Ann. of Math. (2) 58 (1953), 544–547.CrossRefGoogle Scholar
[7]Loos, O.. Über eine Beziehung zwischen Mal'cev-Algebren und Lie-Tripelsystemen. Pacific J. Math. 18 (1966), 553–562.CrossRefGoogle Scholar
[8]Perez de Guzman, I.. Structure theorem for alternative H *-algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437–446.CrossRefGoogle Scholar
[9]Sagle, A. A.. Mal'cev algebras. Trans. Amer. Math. Soc. 101 (1961), 426–458.CrossRefGoogle Scholar
[10]Sagle, A. A.. Simple Mal'cev algebras over fields of characteristic zero. Pacific J. Math. 12 (1962), 1057–1078.CrossRefGoogle Scholar
[11]Schafer, R. D.. An Introduction to Nonassociative Algebras (Academic Press, 1966).Google Scholar
[12]Schue, J. R.. Hilbert space methods in the theory of Lie algebras. Trans. Amer. Math. Soc. 95 (1960), 69–80.CrossRefGoogle Scholar
[13]Schue, J. R.. Cartan decompositions for L *-algebras. Trans. Amer. Math. Soc. 98 (1961), 334–349.Google Scholar