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Proceedings of the American Mathematical Society

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



Integral invariant functions on the nilpotent elements of a semisimple Lie algebra

Author: Michael A. Gauger
Journal: Proc. Amer. Math. Soc. 68 (1978), 161-164
MSC: Primary 17B20; Secondary 22E60
MathSciNet review: 480183
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Abstract: Let L be a semisimple Lie algebra over an algebraically closed field of characteristic zero. It is shown that there is a finitely generated ring R of integral invariant functions such that for nilpotent elements x and y of L, one has x conjugate to y if and only if $ f(x) = f(y)$ for all f in R. The result is analogous to Chevalley's determination of conjugacy classes of semisimple elements by the ring of invariant polynomial functions.

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Keywords: Semisimple Lie algebra, conjugacy, invariant function, nilpotent and semisimple elements
Article copyright: © Copyright 1978 American Mathematical Society