Abstract

Instead of commutative algebras and modules, this chapter studies graded commutative (a.k.a. supercommutative) algebras. Examples of such algebras are the algebras of differential forms and the de Rham cohomology of commutative algebras considered in previous chapters. In this chapter, the theory of differential operators over graded commutative algebras is described. The list of examples includes certain matrix algebras, G-graded commutative algebras, the Grassmann algebra, Poisson dioles, the Batalin–Vilkovisky operators, and the Berezinian for graded algebras.

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