Journal of Applied Mathematics and Statistical Applications

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Journal of Applied Mathematics and Statistical Applications 44 7897 074717

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In mathematics and theoretical physics, a superalgebra may be a Z2-graded algebra. That is, it's algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.

The prefix super- comes from the idea of supersymmetry in theoretical physics. Superalgebras and their representations, supermodules, provide an algebraic framework for formulating supersymmetry. The study of such objects is usually called super algebra. Superalgebras also play a very crucial role in field related of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and superschemes.

An superalgebra which is associative is one whose multiplication is associative. The identity during a unital superalgebra is necessarily even. Unless otherwise specified, all superalgebras during this article are assumed to be associative and unital.

One can also define superalgebras categorically. The category of all R-supermodules forms a monoidal category under the super tensor product with R serving because the unit object.  

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