In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and B are any two pure elements of L and X and Y are any two pure elements of V, then ⋅ X = c 1 A ⋅ X + c 2 B ⋅ X {\displaystyle \cdot X=c_{1}A\cdot X+c_{2}B\cdot X} A ⋅ = c 1 A ⋅ X + c 2 A ⋅ Y {\displaystyle A\cdot =c_{1}A\cdot X+c_{2}A\cdot Y} A ⋅ X = A X {\displaystyle ^{A\cdot X}=^{A}^{X}} [ A, B ] ⋅ X = A ⋅ − A B B ⋅. Wikipedia