English

Differential calculus over N-graded commutative rings

Mathematical Physics 2016-05-24 v1 math.MP

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.

Keywords

Cite

@article{arxiv.1605.07115,
  title  = {Differential calculus over N-graded commutative rings},
  author = {G. Sardanashvily and W. Wachowski},
  journal= {arXiv preprint arXiv:1605.07115},
  year   = {2016}
}

Comments

71 pages. arXiv admin note: substantial text overlap with arXiv:0910.1515, arXiv:0908.1886

R2 v1 2026-06-22T14:07:28.400Z