field of representation theory, a representation of a Liesuperalgebra is an action of Liesuperalgebra L on a Z2-graded vector space V, such that if A and
universal enveloping algebra of a Liesuperalgebra which is a unital, associative superalgebra. Let A be a superalgebra over a commutative ring K. The submodule
semisimple Lie algebra with the structure of a graded Lie algebra. Any parabolic Lie algebra is also a graded Lie algebra. A graded Liesuperalgebra extends
product, a Lie superbracket [ ⋅ , ⋅ ] : A ⊗ A → A {\displaystyle [\cdot ,\cdot ]:A\otimes A\to A} such that (A, [·,·]) is a Liesuperalgebra and the operator