Principal subalgebra: Difference between revisions
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In mathematics, a '''principal subalgebra''' of a complex simple [[Lie algebra]] is a 3-dimensional simple subalgebra whose non-zero elements are [[regular element of a Lie algebra|regular]]. |
In mathematics, a '''principal subalgebra''' of a complex simple [[Lie algebra]] is a 3-dimensional simple subalgebra whose non-zero elements are [[regular element of a Lie algebra|regular]]. |
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A finite-dimensional complex simple Lie algebra has a unique conjugacy class of principal subalgebras, each of which is the span of an [[Sl2-triple| |
A finite-dimensional complex simple Lie algebra has a unique conjugacy class of principal subalgebras, each of which is the span of an [[Sl2-triple|sl<sub>2</sub>-triple]]. |
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==References== |
==References== |
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Revision as of 19:38, 10 August 2013
In mathematics, a principal subalgebra of a complex simple Lie algebra is a 3-dimensional simple subalgebra whose non-zero elements are regular.
A finite-dimensional complex simple Lie algebra has a unique conjugacy class of principal subalgebras, each of which is the span of an sl2-triple.
References
- Bourbaki, Nicolas (2005) [1975], Lie groups and Lie algebras. Chapters 7--9, Elements of Mathematics (Berlin), Berlin, New York: Springer-Verlag, ISBN 978-3-540-43405-4, MR 2109105