English

Differential Calculus over Graded Commutative Algebras and Vector Bundles with Inner Structures

Differential Geometry 2023-12-11 v1 Commutative Algebra

Abstract

In this note we highlight a common origin for many ubiquitous geometric structures, as well as several new ones by using only the functors of differential calculus in A.M Vinogradov's original sense, adapted to special classes of (graded) commutative algebras. Special attention is given to the particularly simple cases of diole and triole algebras and we show the latter environment is the appropriate one to describe calculus in vector bundles in the presence of a vector-valued fiber metric.

Keywords

Cite

@article{arxiv.2312.04842,
  title  = {Differential Calculus over Graded Commutative Algebras and Vector Bundles with Inner Structures},
  author = {Jacob Kryczka},
  journal= {arXiv preprint arXiv:2312.04842},
  year   = {2023}
}

Comments

16 pages

R2 v1 2026-06-28T13:44:45.092Z