Differential calculus over N-graded commutative rings
G. Sardanashvily, W. Wachowski
TL;DR
This paper extends differential calculus to N-graded commutative rings, generalizing classical calculus and connecting it to supergeometry and field theory on graded manifolds.
Contribution
It constructs the Chevalley-Eilenberg differential calculus over N-graded rings, broadening the scope beyond traditional commutative and non-commutative geometries.
Findings
Generalized differential calculus over N-graded rings.
Applicable to Grassmann algebras and supergeometry.
Facilitates field theory on graded manifolds.
Abstract
The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most general case of the differential calculus over rings that is not the non-commutative geometry. Since any N-graded ring possesses the associated Z_2-graded structure, this also is the case of the graded differential calculus over Grassmann algebras and the supergeometry and field theory on graded manifolds.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology