I have seen the definition of the universal enveloping algebra of a Lie algebra is an associative algebra with a unit which satisfies a universal property (always exists and is unique up to isomorphism). I know it should be an associative algebra as it is a left adjoint to the commtator bracket. However, why usually we require it has a unit? Could we define the universal enveloping algebra of a Lie algebra to be an associative algebra without unit?
2026-03-26 19:03:07.1774551787
Why the universal enveloping algebra of a Lie algebra is an associative algebra with a unit?
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