Perfect Lie algebra: Difference between revisions
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{{Lie algebra property}} | {{Lie algebra property}} | ||
{{analogue of property| | |||
{{analogue | old generic context = group| | ||
old specific context = group| | |||
old property = perfect group| | |||
new generic context = Lie algebra| | |||
new specific context = Lie algebra}} | |||
==Definition== | ==Definition== | ||
Latest revision as of 20:26, 24 August 2008
This article defines a property for a Lie algebra
ANALOGY: This is an analogue in Lie algebra of a property encountered in group. Specifically, it is a Lie algebra property analogous to the group property: perfect group
View other analogues of perfect group | View other analogues in Lie algebras of group properties (OR, View as a tabulated list)
Definition
A Lie algebra is said to be perfect if it equals its own commutator ideal. In other words, a Lie algebra is said to be perfect if every element of the Lie algebra is in the ideal generated by commutators.
Also see perfect Lie ring.