Automorphisms on complex simple Lie algebras of order 3

DOI: 10.48129/kjs.10668

Authors

  • Ching-I Hsin Minghsin University of Science and Technology

DOI:

https://doi.org/10.48129/kjs.10668

Keywords:

Lie algebra, automorphism, Dynkin diagram, invariant subalgebra

Abstract

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.

Author Biography

Ching-I Hsin, Minghsin University of Science and Technology

Associate Professor,

Department of Multimedia and Game Development

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.

Published

26-12-2021

Issue

Section

Mathematics