Polyhedral groups in G 2 ( C )

We classify embeddings of the finite groups A 4 , S 4 and A 5 in the Lie group G 2 ( C ) up to conjugation.

[1]  A. Veselov,et al.  Automorphic Lie algebras and modular forms , 2020, 2002.09388.

[2]  Darrin D. Frey,et al.  Conjugacy of Embeddings of Alternating Groups in Exceptional Lie Groups , 2018, Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES.

[3]  C. Draper.  Notes on $G_2$: The Lie algebra and the Lie group , 2017, 1704.07819.

[4]  J. Sanders,et al.  Hereditary automorphic Lie algebras , 2015, Communications in Contemporary Mathematics.

[5]  Jan A. Sanders,et al.  Higher-Dimensional Automorphic Lie Algebras , 2015, Foundations of Computational Mathematics.

[6]  Mark Reeder.  Torsion automorphisms of simple Lie algebras , 2010 .

[7]  J. Sanders,et al.  On the Classification of Automorphic Lie Algebras , 2009, 0912.1697.

[8]  Michael T. Vaughn,et al.  LIE GROUPS AND LIE ALGEBRAS , 2008, Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34.

[9]  A. Mikhailov,et al.  Reduction Groups and Automorphic Lie Algebras , 2004, math-ph/0407048.

[10]  R. Griess,et al.  Classification of finite quasisimple groups which embed in exceptional algebraic groups , 2001 .

[11]  Darrin D. Frey.  Conjugacy of Alt_5 and SL(2, 5) Subgroups of E_8(C) , 2001 .

[12]  R. Griess.  Basic conjugacy theorems forG2 , 1995 .

[13]  M. Larsen.  On the conjugacy of element-conjugate homomorphisms , 1994 .

[14]  I. Stewart,et al.  Infinite-dimensional Lie algebras , 1974 .

[15]  V. Kats,et al.  Automorphisms of finite order of semisimple Lie algebras , 1969 .

[16]  E. Cartan,et al.  La géométrie des groupes simples , 1927 .

[17]  Darrin D. Frey,et al.  6D SCFTs and the Classification of Homomorphisms , 2020 .

[18]  A. Cohen,et al.  On finite simple subgroups of the complex Lie group of type $E_8$ , 1987 .

[19]  A. Cohen,et al.  Finite subgroups of G2(C) , 1983 .