Deformation complexes of algebraic operads and their applications

Given a reduced cooperad C, we consider the 2-colored operad Cyl(C) which governs diagrams U: V -> W, where V, W are Cobar(C)-algebras, and U is an infinity-morphism. We then investigate the deformation complexes of Cyl(C) and Cobar(C). Our main result is that the restriction maps between between the deformation complexes Der'(Cyl(C)) and Der'(Cobar(C)) are homotopic quasi-isomorphisms of filtered Lie algebras. We show how this result may be applied to modifying diagrams of homotopy algebras by derived automorphism. We then recall that Tamarkin's construction gives us a map from the set of Drinfeld associators to the homotopy classes of Lie infinity quasi-isomorphisms for Hochschild cochains of a polynomial algebra. Due to results of V. Drinfeld and T. Willwacher, both the source and the target of this map are equipped with natural actions of the Grothendieck-Teichmueller group GRT. We use our earlier results to prove that this map from the set of Drinfeld associators to the set of homotopy classes of Lie infinity quasi-isomorphisms for Hochschild cochains is GRT-equivariant.

Grantor dc:publisher

Temple University. Libraries

Year dc:date.issued

2015

Author dc:creator

• Paljug, Brian

Advisor dc:contributor.advisor

• Dolgushev, Vasily

Committee members dc:contributor.committeemember

• Futer, David
• Lorenz, Martin, 1951-
• Block, Jonathan, 1960-

• Mathematics
• Deformation quantization
• Grothendieck-Teichmueller Group
• Homological algebra
• Operads

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Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

eng

Dc Identifier Other

931912253

OAI identifier oai:identifier

oai:scholarshare.temple.edu:20.500.12613/3379