Lie antialgebras is a class of supercommutative algebras recently appeared in
symplectic geometry. We define the notion of enveloping algebra of a Lie
antialgebra and study its properties. We show that every Lie antialgebra is
canonically related to a Lie superalgebra and prove that its enveloping algebra
is a quotient of the enveloping algebra of the corresponding Lie superalgebra.

We consider $\G$-graded commutative algebras, where $\G$ is an abelian group.
Starting from a remarkable example of the classical algebra of quaternions and,
more generally, an arbitrary Clifford algebra, we develop a general viewpoint
on the subject. We then give a recent classification result and formulate an
open problem.