- #1

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Let G be a Matrix Lie group. The group acts on itself by left multiplication, i.e,

L

_{g}h = gh where g,h ∈ G

Which corresponds to a translation by g.

Is this an example of a module over a ring where g ∈ R and h ∈ M and the scalar multiplication is interpreted as a linear map (matrix multiplication)?

If so, how does one interpret the Lie bracket [x,y] in terms rings and modules (or can one)?