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.


References [Enhancements On Off] (What's this?)

  • [1] Michael A. Gauger, Conjugacy in a semisimple Lie algebra is determined by similarity under fundamental representations, J. Algebra 48 (1977), no. 2, 382–389. MR 0453827
  • [2] Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 0158024
  • [3] C. C. MacDuffe, The theory of matrices, Chelsea, New York, 1946.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0480183-6
Keywords: Semisimple Lie algebra, conjugacy, invariant function, nilpotent and semisimple elements
Article copyright: © Copyright 1978 American Mathematical Society