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Spectral resolution of the identity for matrices of elements of a lie algebra

Published online by Cambridge University Press:  17 February 2009

H. S. Green
H. S. Green
Affiliation:
Department of Mathematical Physics, The University of Adelaide, Adelaide, S.A. 5000, Australia.
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Abstract

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This is an application of the characteristic identity satisfied by matrices whose elements are also elements of a semi-simple Lie algebra. Generalized eigenvectors are determined for matrices consisting of generators of GL(n), O(n) and Sp(n), and it is shown how to resolve the identity into idempotents constructed from such eigenvectors. By this means rather general functions of the matrices may be defined. It is also shown how to determine traces of such functions, in terms of the invariants of the Lie algebra.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 2 , December 1975 , pp. 129 - 139
Copyright
Copyright © Australian Mathematical Society 1975

References

[1] For a modern practical introduction to Lie algebras, see Gilmore, R., Lie Groups, Lie Algebras and Some of their Applications, (Wiley, New York, 1974).CrossRefGoogle Scholar
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[4]Green, H. S., J. Math. Phys. 12, 2106 (1971).CrossRefGoogle Scholar
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