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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Is there any example of a Lie algebra which is not a derivation algebra?
I'm just studying Lie algebras. If $A$ is a $k$-algebra (not necessarily Lie or associative, just a bilinear law), it is straightforward to check that any derivation algebra of $A$ is a Lie algebra. I …