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A spectral sequence for the homology of a finite algebraic delooping

Published online by Cambridge University Press:  20 May 2014

Birgit Richter  and
Stephanie Ziegenhagen
Birgit Richter
Affiliation:
Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany, birgit.richter@uni-hamburg.de
Stephanie Ziegenhagen
Affiliation:
Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany, stephanie.ziegenhagen@uni-hamburg.de
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Abstract

In the world of chain complexes En-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic En-homology of an En-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher order Hochschild homology in terms of derived functors of indecomposables of Gerstenhaber algebras and as the homology of exterior and symmetric powers of derived Kähler differentials.

Keywords

En-homologyHochschild cohomologyAndré-Quillen homologyΠ-AlgebrasGrothendieck spectral sequenceHodge decompositionPrimary 16E4018G40Secondary 55P35
Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 3 , June 2014 , pp. 563 - 599
Copyright
Copyright © ISOPP 2014 

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