THESIS
2017
Abstract
In this thesis, we consider a general construction of dihedral subgroups D
n, in the auto-morphism group of a complex finite-dimensional simple Lie algebra g. Our main results
are based on Kac's classification results of finite order automorphisms on g and a classic
result on classification of Z-gradings on g. A dihedral subgroup D
n in the automorphism group of g can be defined by an order n automorphism σ and an order 2 automorphism r
of g satisfying the relation rσ = σ
-1r. The key point to find the generators (σ, r) of the
dihedral subgroups is to fix the order n automorphism σ and extend an involution r
0 on the fixed point of σ to r on the whole Lie algebra g. Finally, We give a complete list of classification of (σ, r) generating D
3-subgroups in the automorphism group of g....[
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In this thesis, we consider a general construction of dihedral subgroups D
n, in the auto-morphism group of a complex finite-dimensional simple Lie algebra g. Our main results
are based on Kac's classification results of finite order automorphisms on g and a classic
result on classification of Z-gradings on g. A dihedral subgroup D
n in the automorphism group of g can be defined by an order n automorphism σ and an order 2 automorphism r
of g satisfying the relation rσ = σ
-1r. The key point to find the generators (σ, r) of the
dihedral subgroups is to fix the order n automorphism σ and extend an involution r
0 on the fixed point of σ to r on the whole Lie algebra g. Finally, We give a complete list of classification of (σ, r) generating D
3-subgroups in the automorphism group of g.
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