Automorphisms on complex simple Lie algebras of order 3
DOI: 10.48129/kjs.10668
DOI:
https://doi.org/10.48129/kjs.10668Keywords:
Lie algebra, automorphism, Dynkin diagram, invariant subalgebraAbstract
For complex simple Lie algebras, the article provides classification of all automorphisms of order 3. The method is an extension of Dynkin diagrams, so that the classification is a listing of diagrams which represent automorphisms of order 3. This work extends an earlier result on automorphisms of order 2. As an application, it shows that for automorphisms of orders 2 and 3 only, the invariant subalgebra determines the automorphism.
References
M. K. Chuah, Finite order automorphisms on real simple Lie algebras, Trans. Amer. Math. Soc. 364 (2012), 3715-3749.
S. Helgason, Differential Geometry, Lie Groups, and Symmetric
Spaces, Graduate Studies in Math. vol. 34, Amer. Math. Soc.,
Providence 2001.
J. E. Humphreys, Introduction to Lie algebras and representation theory, Grad. Text in Math. 9, Springer 1973.
V. G. Kac, Infinite Dimensional Lie Algebras, 3rd. ed., Cambridge Univ. Press, Cambridge 1990.
J. Wolf and A. Gray, Homogeneous spaces defined by Lie group automorphisms, I and II, J. Diff. Geom. 2 (1968), 77-159.
