Infinity-enhancing of Leibniz algebras
Artikel i vetenskaplig tidskrift, 2020

We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies (Bonezzi and Hohm in Commun Math Phys 377:2027-2077, 2020), and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz algebra. Moreover, by a theorem of Getzler, this differential graded Lie algebra canonically induces an L-infinity-algebra structure on the suspension of the underlying chain complex. We explicitly give the brackets to all orders and show that they agree with the partial results obtained from the infinity-enhanced Leibniz algebras in Bonezzi and Hohm (Commun Math Phys 377:2027-2077, 2020).

Författare

Sylvain Lavau

Université Paris Diderot

Jakob Palmkvist

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Örebro universitet

Letters in Mathematical Physics

0377-9017 (ISSN) 1573-0530 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s11005-020-01324-7

Mer information

Senast uppdaterat

2020-10-26