Cohomology of Lie Coalgebras

Lazarev, Andrey and Chuang, Joseph and Sheng, Yunhe and Tang, Rong (2025) Cohomology of Lie Coalgebras. Journal of Noncommutative Geometry. ISSN 1661-6952 (In Press)

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Abstract

A Koszul duality-type correspondence between coderived categories of conilpotent differential graded Lie coalgebras and their Chevalley-Eilenberg differential graded algebras is established. This gives an interpretation of Lie coalgebra cohomology as a certain kind of derived functor. A similar correspondence is proved for coderived categories of commutative cofibrant differential graded algebras and their Harrison differential graded Lie coalgebras.