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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[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.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
17B20,
22E60

Retrieve articles in all journals with MSC: 17B20, 22E60

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