2015/12/31 by Maxime Fairon · 1 citation
Mathematics · Physics and Astronomy · #math.DG #math-ph #math.MP #msc:58A50 #msc:51-02
paper · pdf · doi:10.1007/s40879-017-0138-4
published as Eur. J. Math. 3 (2017), no. 2, 208-222 · 15 pages, to appear in European Journal of Mathematics
arxiv created 2017/03/14 · arxiv updated 2018/03/29
This paper aims at setting out the basics of ℤ-graded manifolds theory. We introduce ℤ-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric algebra to define functions is made clear. Moreover, we define vector fields and exhibit their graded local basis. The paper also reviews some correspondences between differential Z-graded manifolds and algebraic structures.