RT Journal Article
T1 Lie models of homotopy automorphism monoids and classifying fibrations
A1 Félix, Yves
A1 Fuentes Rumí, Mario
A1 Murillo-Mas, Aniceto
K1 Lie, Algebras de
AB Given X a finite nilpotent simplicial set, consider theclassifying fibrationsX → B aut∗G(X) → B autG(X) and X → Z → B aut∗π (X)where G and π denote, respectively, subgroups of the free andpointed homotopy classes of free and pointed self homotopyequivalences of X which act nilpotently on H∗(X) and π∗(X).We give algebraic models, in terms of complete differentialgraded Lie algebras (cdgl’s), of the rational homotopy type ofthese fibrations. Explicitly, if L is a cdgl model of X, there areconnected sub cdgl’s DerGL and DerΠL of the Lie algebra ofderivations of L such that the geometrical realizations of thesequences of cdgl morphismsL ad→ DerGL → DerGL  ̃×sL and L → L  ̃×DerΠL → DerΠLhave the rational homotopy type of the above classifyingfibrations. Among the consequences we also describe in cdgl*We give algebraic models, in terms of complete differential graded Lie algebras (cdgl's), of the rational homotopy type of these fibrations. Explicitly, if L is a cdgl model of X, there are connected sub cdgl's  and  of the Lie algebra of derivations of L such that the geometrical realizations of the sequences of cdgl morphismshave the rational homotopy type of the above classifying fibrations. Among the consequences we also describe in cdgl terms the Malcev -completion of G and π together with the rational homotopy type of the classifying spaces BG and Bπ.
PB Elsevier
YR 2022
FD 2022-06-25
LK https://hdl.handle.net/10630/24331
UL https://hdl.handle.net/10630/24331
LA spa
NO Félix, Yves,  Fuentes Rumí, Mario,  Murillo-Mas, Aniceto; Lie models of homotopy automorphism monoids and classifying fibrations. Advances in Mathematics Volume 402, 25 June 2022, 108359. https://doi.org/10.1016/j.aim.2022.108359
NO Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026