Simple representations of $L=C$

Question

What are the simple representations of the one dimensional Lie algebra $L=C$? This is for study so any help would be great.

Dietrich Burde · Accepted Answer · 2019-12-07T15:16:52.933

1

All simple representations of finite-dimensional solvable complex Lie algebras are $1$-dimensional because of Lie's Theorem. Clearly, the $1$-dimensional Lie algebra is solvable, compare with

Is the one-dimensional Lie algebra L=C semisimple?.

edited Dec 07 '19 at 15:16

answered Dec 07 '19 at 15:09

Dietrich Burde

130,978

I can understand how it is solvable since it is abelian and thus falls under Lies theorem. What would be an example of a simple representation then of it? @Dietrich – ConnectNumbers66 Dec 12 '19 at 20:19
The trivial $1$-dimensional representation. – Dietrich Burde Dec 14 '19 at 20:41

Simple representations of $L=C$

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