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 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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-  Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 0158024, https://doi.org/10.2307/2373130
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- M. Gauger, Conjugacy in a semi-simple Lie algebra is determined by similarity under fundamental representations, J. Algebra (to appear). MR 0453827 (56:12080)
- B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327-404. MR 0158024 (28:1252)
- C. C. MacDuffe, The theory of matrices, Chelsea, New York, 1946.
Keywords: Semisimple Lie algebra, conjugacy, invariant function, nilpotent and semisimple elements
Article copyright: © Copyright 1978 American Mathematical Society