[[Lie algebras MOC]]
# Module over a Lie algebra
A **module over a Lie algebra** $\mathfrak{g}$ or $\mathfrak{g}$-**module** is an abuse of terminology for a vector space carrying a [[Lie algebra representation]].[^frenk] #m/def/lie
The actual [[module]] being invoked is one over the [[Universal enveloping algebra]] of the [[Lie algebra]].

  [^frenk]: See 1988, [[@frenkelVertexOperatorAlgebras1988|Vertex operator algebras and the Monster]], pp. 5–6 for an example of this usage.

## See also

- When one talks of a tensor product of such modules, one usually means the [[Tensor product of Lie algebra representations]].

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