Infinity-enhancing of Leibniz algebras
Journal article, 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).


Sylvain Lavau

Paris Diderot University

Jakob Palmkvist

Örebro University

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Letters in Mathematical Physics

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

Vol. 110 11 3121-3152

Subject Categories

Algebra and Logic


Mathematical Analysis



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