# what is the difference between algebra and Lie algebra

I am writting a simple repport on Lie algebras and I thought I could start just with a ''strandard'' simple definition of algebra to make an introduction for Lie algebra and then relate these 2 definitions somehow with one another.

Does anyone know how I can do it in a descriptive way?

Thank you

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Well, certainly a Lie algebra is not in general an algebra, since Lie brackets are not associative in general. The simplest relationship between associative algebras and Lie algebras is that given any algebra $A$ over a field $k$, defining $[x, y] = xy - yx$ for $x, y \in A$ turns $A$ into a Lie algebra.