[[Lie algebra]]
# Abelian Lie algebra

A [[Lie algebra]] $\mathfrak{g}$ is said to be **abelian** iff $[\mathfrak{g,\mathfrak{g}}]=0$. #m/def/lie 
[[Away from 2]] this is the same as requiring the Lie bracket to commute.

## Properties

- Every one-dimensional Lie algebra is abelian.

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#state/tidy | #lang/en | #SemBr