The complex of looped diagrams and natural operations on Hochschild homology

Angela Klamt

The complex of looped diagrams and natural operations on Hochschild homology

Angela Klamt

Abstract

In this thesis natural operations on the (higher) Hochschild complex of a given family of algebras are investigated. We give a description of all formal operations (in the sense of Wahl) for the class of commutative algebras using Loday's lambda operation, Connes' boundary operator and shue products. Furthermore, we introduce a dg-category of looped diagrams and show how to generate operations on the Hochschild complex of commutative Frobenius algebras out of these. This way we recover all operations known for symmetric Frobenius algebras (constructed via Sullivan diagrams), all the formal operations for commutative algebras (as computed in the rst part of the thesis) and a shifted BV structure which has been investigated by Abbaspour earlier. We prove that this BV structure comes from a suspended Cacti operad sitting inside the complex of looped diagrams. Last, we eneralize the setup of formal operations on Hochschild homology to higher Hochschild homology. We also generalize statements about the formal operations and give smaller models for the formal operations on higher Hochschild homology in certain cases.

Originalsprog	Engelsk

Forlag	Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ISBN (Trykt)	978-87-7078-981-3
Status	Udgivet - 2013

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Citationsformater

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