Spark algebras and quantum groups


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


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


          @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


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.)


Zoom link https://pitp.zoom.us/j/93746215441?pwd=YjdhaDNFeko3VDVKQW5ZV1MzL1cvUT09