We compute Ext groups between Soergel Bimodules associated to the infinite/finite dihedral group for a realization in characteristic 0 and show that they are free right 𝖱−modules with an explicit basis. We then give a diagrammatic presentation for the corresponding monoidal category of Ext-enhanced Soergel Bimodules. As applications, we compute reduced triply graded link homology 𝐇̅𝐇̅𝐇̅ of the connect sum of two Hopf links as an 𝖱−module and show that the Poincare series for the Hochschild homology of Soergel Bimodules of finite dihedral type categorifies Gomi's trace for finite dihedral groups.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/9dyf-r781 |
| Date | January 2024 |
| Creators | Li, Cailan |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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