A Lie algebra is defined to be a vector space with a skew symmetric bilinear multiplication which satisfies the Jacobi identity.
More generally, a Lie algebra is an object,
-modules) with a morphism that is skew-symmetric and satisfies the Jacobi identity.
A Lie conformal algebra, then, is an object
-modules with morphism called the lambda bracket, which satisfies modified versions of bilinearity, skew-symmetry and the Jacobi identity: One can see that removing all the lambda's, mu's and partials from the brackets, one simply has the definition of a Lie algebra.
with lambda bracket given by In fact, it has been shown by Wakimoto that any Lie conformal algebra with lambda bracket satisfying the Jacobi identity on one generator is actually the Virasoro conformal algebra.