Opened Access Derived homotopy algebras
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Author: Maes, Jeroen
Director: Muro Jiménez, Fernando
Department: Instituto de Matemáticas de la Universidad de Sevilla (Antonio de Castro Brzezicki)
Date: 2016-10-28
Document type: Doctoral Thesis
Abstract: Derived A-algebras are derived and homotopy invariant versions of differential graded algebras. They were introduced by Steffen Sagave in 20 0 in order to construct minimal models for diferential graded algebras over arbitrary commutative rings. Muriel Livernet, Constanze Roitzheim, and Sarah Whitehouse showed in 2013 how they can be viewed as algebras over the minimal model of the operad encoding bicomplexes with a compatible associative multiplication. We extend their work for the associative operad to a general quadratic Koszul operad O satisfying standard projectivity assumptions. This leads to the new notion of derived homotopy O-algebra, where minimal models for O-algebras are defined. We explicitly compute generating operations and relations when O is the associative operad, the commutative operad, and the operad encoding Lie algebras.
Cite: Maes, J. (2016). Derived homotopy algebras. (Tesis doctoral inédita). Universidad de Sevilla, Sevilla.
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