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pinball1970
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I would feel like a fraud just liking your post as that would suggest I understood it so I will say thanks for explaining this way first. Then like it.fresh_42 said:A non associative algebra is a baric algebra if and only if it has an ideal of codimension one.
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More generally it can be shown that Lie algebras cannot be baric algebras.
This sounds reasonable each on its own, but what about solvable Lie algebras which do have an ideal of codimension one? E.g. ##\mathcal{A} = \langle X,Y\,|\,[X,Y]=Y\rangle##.
https://de.wikipedia.org/wiki/Baric-Algebra