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The Derived Deligne Conjecture

Aguilar Martin, Javier (2024) The Derived Deligne Conjecture. Doctor of Philosophy (PhD) thesis, University of Kent,. (doi:10.22024/UniKent/01.02.105426) (KAR id:105426)

Abstract

We study the operad of derived A∞-algebras from a new point of view in order to find a derived version of the Deligne conjecture. We start by defining the brace structure on an operad of graded R-modules using operadic suspension, which we describe in depth for the first time as a functor, and use it to define A∞-algebra structures on certain operads, with the endomorphism operad as our main example. This construction provides us with an operadic context from which A∞-algebras arise in a natural way and allows us to generalize the Lie algebra structure on the Hochschild complex of an A∞-algebra. Next, we generalize these con structions to operads of bigraded R-modules, introducing a totalization functor. This allows us to generalize a Lie algebra structure on the to tal complex of a derived A∞-algebra. This construction and the use of some enriched categories allow us to obtain new versions of the Deligne conjecture.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Roitzheim, Constanze
Thesis advisor: Whitehouse, Sarah
DOI/Identification number: 10.22024/UniKent/01.02.105426
Uncontrolled keywords: operads; homotopy theory; homological algebra
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: University of Kent (https://ror.org/00xkeyj56)
SWORD Depositor: System Moodle
Depositing User: System Moodle
Date Deposited: 25 Mar 2024 10:10 UTC
Last Modified: 26 Mar 2024 16:05 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/105426 (The current URI for this page, for reference purposes)

University of Kent Author Information

Aguilar Martin, Javier.

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