Koszul dual of a commutative algebraGeneral observation:
Consider the case when is a commutative algebra. This means that includes all antisymmetric tensors.
is a universal enveloping of a Lie algebra.
Example: If is the algebra of polynomials of variables , then the dual Lie algebra is the algebra of antisymmetric polynomials . This is the universal enveloping of the Lie superalgebra .