Cocommutative algebras : homotopy theory and Koszul duality

• DOI: 10.48550/arxiv.1403.0774
• Publication Date: 2016-01-01
• Authors: Chuang, Joseph; Lazarev, Andrey; Mannan, Wajid Hassan
• Keywords: Mathematics - Quantum Algebra; FOS: Mathematics; Algebraic Topology (math.AT); Quantum Algebra (math.QA); Mathematics - Algebraic Topology; 0101 mathematics; QA; 01 natural sciences; 510

38 pages<br/>We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.<br/>