Borel–de Siebenthal theory
In mathematics, Borel–de Siebenthal theory describes the closed connected subgroups of a compact Lie group that have maximal rank, i.e. contain a maximal torus. It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the theory in 1949. Each such subgroup is the identity component of the centralizer of its center. They can be described recursively in terms of the associated root system of the group. The subgroups for which the corresponding homogeneous space has an invariant complex structure correspond to parabolic subgroups in the complexification of the compact Lie group, a reductive algebraic group.
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Borel–de Siebenthal theory
In mathematics, Borel–de Siebenthal theory describes the closed connected subgroups of a compact Lie group that have maximal rank, i.e. contain a maximal torus. It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the theory in 1949. Each such subgroup is the identity component of the centralizer of its center. They can be described recursively in terms of the associated root system of the group. The subgroups for which the corresponding homogeneous space has an invariant complex structure correspond to parabolic subgroups in the complexification of the compact Lie group, a reductive algebraic group.
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In mathematics, Borel–de Siebe ...... , a reductive algebraic group.
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THEOREM. The maximal connected ...... up to conjugacy have the form
THEOREM. Up to equivalence the ...... ots −α0 and all αj with j ≠ i.
• C'G1 for m'i = 1
• C'G1 for m'i a prime.
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In mathematics, Borel–de Siebe ...... , a reductive algebraic group.
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Borel–de Siebenthal theory
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