Editing Superalgebra (section)

{{Short description|Algebraic structure used in theoretical physics}}
In [[mathematics]] and [[theoretical physics]], a '''superalgebra''' is a '''Z'''<sub>2</sub>-[[graded algebra]].<ref>{{harvnb|Kac|Martinez|Zelmanov|2001|p=3}}</ref> That is, it is an [[algebra (ring theory)|algebra]] over a [[commutative ring]] or [[field (mathematics)|field]] with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.

The prefix ''super-'' comes from the theory of [[supersymmetry]] in theoretical physics. Superalgebras and their representations, [[supermodule]]s, provide an algebraic framework for formulating supersymmetry. The study of such objects is sometimes called [[super linear algebra]]. Superalgebras also play an important role in related field of [[supergeometry]] where they enter into the definitions of [[graded manifold]]s, [[supermanifold]]s and [[superscheme]]s.