Lie theory of multiplicative tensors
Differential Geometry
2021-09-15 v2
Abstract
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorphic structures, obtained through a unifying and conceptual method. We also give a full treatment of multiplicative vector-valued forms, particularly Nijenhuis operators and related structures.
Keywords
Cite
@article{arxiv.1705.08579,
title = {Lie theory of multiplicative tensors},
author = {Henrique Bursztyn and Thiago Drummond},
journal= {arXiv preprint arXiv:1705.08579},
year = {2021}
}
Comments
54 pages. v2: minor corrections, typos fixed, references updated