L ∞ algebras and tensor hierarchies in Exceptional Field Theory and Gauged Supergravity

Abstract We show how the gauge and field structure of the tensor hierarchies in Double and E 7(7) Exceptional Field Theory fits into L ∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.