[[Lie algebras MOC]]
# Graded Lie algebra
Let $(\mathfrak{A}, +)$ be a (necessarily abelian) [[monoid]].
A $\mathfrak{A}$-**graded Lie algebra** is an example of a [[graded algebra]], #m/def/lie
i.e.
$$
\begin{align*}
[A_{\alpha}, A_{\beta}] \sube A_{\alpha + \beta}
\end{align*}
$$

## Properties

- [[Universal enveloping algebra#Graded structure|Universal enveloping algebra of a graded Lie algebra]]

## Category of graded Lie algebras

See [[Category of graded Lie algebras]].

## See also

- [[Graded structure]]

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