In mathematics, an Engel subalgebra of a
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
with respect to some element ''x'' is the subalgebra of elements annihilated by some power of ad ''x''. Engel subalgebras are named after
Friedrich Engel. For finite-dimensional Lie algebras over infinite fields the minimal Engel subalgebras are the
Cartan subalgebra
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra \mathfrak of a Lie algebra \mathfrak that is self-normalising (if ,Y\in \mathfrak for all X \in \mathfrak, then Y \in \mathfrak). They were introduced by à ...
s.
See also
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Engel's theorem
In representation theory, a branch of mathematics, Engel's theorem states that a finite-dimensional Lie algebra \mathfrak g is a nilpotent Lie algebra_if_and_only_if_for_each_X_\in_\mathfrak_g,_the_adjoint_representation_of_a_Lie_algebra.html" "ti ...
References
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{{algebra-stub
Lie algebras