Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T01:36:27.975Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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