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Models for classifying spaces and derived deformation theory
Author(s) -
Lazarev A.
Publication year - 2014
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdt069
Subject(s) - mathematics , homotopy , cohomology , pure mathematics , functor , algebraic structure , deformation theory , algebra over a field , homotopy category , homological algebra , abelian group , algebraic number , abelian category , mathematical analysis
Using the theory of extensions of L ∞ algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the Chevalley–Eilenberg and Harrison cohomology. We also investigate the algebraic structure of the Chevalley–Eilenberg complexes of L ∞ algebras and show that they possess, along with the Gerstenhaber bracket, an L ∞ structure that is homotopy abelian.