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Hilbert space methods in the theory of Jordan algebras. II

Published online by Cambridge University Press:  24 October 2008

C. Viola Devapakkiam  and
P. S. Rema
C. Viola Devapakkiam
Affiliation:
Arts College, Dindigul, Tamil Nadu and Ramanujan Institute, Madras
P. S. Rema
Affiliation:
Arts College, Dindigul, Tamil Nadu and Ramanujan Institute, Madras
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Extract

In this paper we consider the classification problem for separable special simple J*-algebras (cf. (8)). We show, using a result of Ancochea, that if is the (finite-dimensional) Jordan algebra of all complex n × n matrices and ø a Jordan isomorphism of onto a special J*-algebra J then An can be given the structure of an H*-algebra such that ø is a *-preserving isomorphism of the J*-algebra onto J. This result enables us to construct explicitly a canonical basis for a finite-dimensional simple special J*-algebra isomorphic to a Jordan algebra of type I from which we also obtain canonical bases for special simple finite-dimensional J*-algebras isomorphic to Jordan algebras of type II and III.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 2 , March 1976 , pp. 307 - 319
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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