Tensor product of algebras

Tensor product of a Lie algebra and a commutative algebra

Let be a Lie algebra and be a commutative algebra, both over . Then their tensor product algebra is also a Lie algebra. lie

Proof

That the product on is alternating follows immediately. For the ^Jacobi note

as required.

Note that if is unital, then we have the injective Lie algebra homomorphism

Functoriality

This construction forms a functor .

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