Derived Lie algebras in geometry and topology

Lie algebras have been a fundamental tool to describe symmetry in mathematics since the nineteenth century. In the past few years, several generalizations of the notion of a Lie algebra inspired by homotopy theory have surfaced, such as differential graded Lie algebras, spectral Lie algebras and partition Lie algebras. Here the basic objects are no longer rigid but can be deformed in interesting ways. This special issue aims to cover some current developments related to these newly found ‘derived Lie algebras’ and showcase some of their applications to algebra, geometry and topology. This article is part of the theme issue ‘Derived Lie algebras in geometry and topology’.