# Spark algebras and quantum groups

### APA

Dimofte, T. (2023). Spark algebras and quantum groups. Perimeter Institute. https://pirsa.org/23120034

### MLA

Dimofte, Tudor. Spark algebras and quantum groups. Perimeter Institute, Dec. 07, 2023, https://pirsa.org/23120034

### BibTex

@misc{ pirsa_PIRSA:23120034, doi = {10.48660/23120034}, url = {https://pirsa.org/23120034}, author = {Dimofte, Tudor}, keywords = {Mathematical physics}, language = {en}, title = {Spark algebras and quantum groups}, publisher = {Perimeter Institute}, year = {2023}, month = {dec}, note = {PIRSA:23120034 see, \url{https://pirsa.org}} }

Tudor Dimofte University of Edinburgh

## Abstract

I will discuss an explicit way to construct Hopf algebras and quasi-triangular Hopf algebras (their Drinfeld doubles) within 3d TQFT, using extended operators on boundary conditions -- dubbed `spark' algebras. The representation categories of these algebras capture boundary and bulk line operators. Overall, the construction realizes Tannakian duality geometrically; in perturbative TQFT's, it is closely connected to the holographic Koszul duality of Costello and Paquette. I'll illustrate the construction for Dijkgraaf-Witten theory (a.k.a. gauge theory with finite gauge group), and then sketch an application to the B-type topological twist of 3d N=4 gauge theories, which initially motivated these investigations. (Work in progress with T. Creutzig and W. Niu.)

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