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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Diagonalization in compact Lie algebras and a new proof of a theorem of Kostant


Author: N. J. Wildberger
Journal: Proc. Amer. Math. Soc. 119 (1993), 649-655
MSC: Primary 22E60
DOI: https://doi.org/10.1090/S0002-9939-1993-1151817-6
MathSciNet review: 1151817
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Abstract: We exhibit a simple algorithmic procedure to show that any element of a compact Lie algebra is conjugate to an element of a fixed maximal abelian subalgebra. An estimate of the convergence of the algorithm is obtained. As an application, we provide a new proof of Kostant's theorem on the projection of orbits onto a maximal abelian subalgebra.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1151817-6
Keywords: Diagonalization, compact Lie algebra, Kostant's theorem
Article copyright: © Copyright 1993 American Mathematical Society