From differential crossed modules to tensor hierarchies
Abstract
Leibniz algebras have been increasingly used in gauging procedures in supergravity, as it can be shown that embedding tensors naturally induce such algebraic structures. Recent mathematical interpretations of these gauging procedures involve what are called 'LieLeibniz triples', of which differential crossed modules are particular cases. This paper is devoted to presenting a new construction of tensor hierarchies from this point of view, that we deem clearer and more straightforward than previous derivations. Moreover, this new construction is a significant improvement since it enables us to draw out a relationship between tensor hierarchies and differential crossed modules. We show in particular that there exists a faithful injectiveonobjects functor from semistrict LieLeibniz triples to differential graded Lie algebras (dgLa), whose restriction to differential crossed modules is the canonical assignment associating to any differential crossed module its corresponding unique 3term differential graded Lie algebra. We stress that such a functorial construction suggests the existence of further welldefined Leibniz gauge theories.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.07838
 Bibcode:
 2020arXiv200307838L
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Algebraic Topology
 EPrint:
 v2 (important changes), 44 pages, comments welcome