(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How can you find all inequivalent (non-isomorphic) 2D Lie algebras just by an analysis of the commutator?

2. Relevant equations

$$[X,Y] = \alpha X + \beta Y$$

3. The attempt at a solution

I considered three cases: ##\alpha = \beta \neq 0, \alpha = 0## or ##\beta = 0, \alpha = \beta = 0##. I found that there can only be one 2D Lie algebra with commutator ##[X,Y] = X##. I'm not sure how to arrive at this answer. Any help is appreciated T_T. Thanks!!!!

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# Homework Help: All possible inequivalent Lie algebras

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