Tensor hierarchies and Leibniz algebras
High Energy Physics - Theory
2021-11-11 v7 Mathematical Physics
math.MP
Abstract
Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically associate a tensor hierarchy to any Loday algebra. By formalizing the construction that is performed in supergravity, we build this tensor hierarchy explicitly. We show that this tensor hierarchy can be canonically equipped with a differential graded Lie algebra structure that coincides with the one that is found in supergravity theories.
Cite
@article{arxiv.1708.07068,
title = {Tensor hierarchies and Leibniz algebras},
author = {Sylvain Lavau},
journal= {arXiv preprint arXiv:1708.07068},
year = {2021}
}
Comments
v6. (important typo corrected), 53 pages, final version