Cohomology of Lie coalgebras
Joseph Chuang, Andrey Lazarev, Yunhe Sheng, Rong Tang
TL;DR
This paper establishes a duality between categories of Lie coalgebras and their Chevalley-Eilenberg algebras, providing a new perspective on Lie coalgebra cohomology as a derived functor.
Contribution
It introduces a Koszul duality-type correspondence linking Lie coalgebras and their Chevalley-Eilenberg algebras, expanding the understanding of their cohomological properties.
Findings
Derived functor interpretation of Lie coalgebra cohomology
Duality between coderived categories of Lie coalgebras and Chevalley-Eilenberg algebras
Correspondence for commutative cofibrant DGAs and Harrison Lie coalgebras
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology