# Superalgebra

A

**superalgebra** is a

graded algebra equipped with a product called the superLie bracket such that if A and B are "pure" in the grading, then [A,B}=(-1)

^{AB}[B,A} (supercommutivity) and (-1)

^{CA}[A,[B,C}}+(-1)

^{AB}[B,[C,A}}+(-1)

^{BC}[C,[A,B}}=0(superJacobi identity).

See also Supergroup (physics), Supersymmetry, Quantum group, Lie algebra, Superspace, Grassmann algebra, Anyonic Lie algebra, Anyspace

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