TY - BOOK

T1 - The complex of looped diagrams and natural operations on Hochschild homology

AU - Klamt, Angela

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99121972826705763

M3 - Ph.D. thesis

SN - 978-87-7078-981-3

BT - The complex of looped diagrams and natural operations on Hochschild homology

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -