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  "body": "\n## Summary\n\nA superalgebra is an algebra graded by $\\Z/2\\Z$: it splits as an even part and an odd part, and the product adds parities.\nIt is the algebraic setting for supersymmetry, where even elements behave like ordinary commuting quantities and odd elements like anticommuting ones.\nThe [[exterior algebra|0MDMZ965VE]] and [[Clifford algebras|A38B1QFK20]] are basic examples, and Lie superalgebras are the corresponding nonassociative notion.\nMany constructions, such as tensor products and commutators, acquire a sign $(-1)^{\\abs{a}\\abs{b}}$ when two odd elements are moved past each other.\n\n## Explanations\n\n### L1 human\n\nSort the elements of an algebra into two kinds, even and odd, like even and odd numbers.\nThe product follows the rule for adding parities: even times even and odd times odd are even, and even times odd is odd.\nIn the exterior algebra of the plane, with basis $1, e_1, e_2, e_1 e_2$, the even part is spanned by $1$ and $e_1 e_2$ and the odd part by $e_1$ and $e_2$.\nThere $e_1 e_2 = -e_2 e_1$: two odd elements anticommute, which is the typical \"super\" sign rule.\n",
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