Strands algebras and the affine highest weight property for equivariant hypertoric categories. (English) Zbl 1504.14088
The authors show that the equivariant hypertoric convolution algebras introduced by Braden-Licata-Proudfoot-Webster are affine quasi hereditary and compute the Ext groups between standard modules, showing that a number of new homological results about the bordered Floer algebras of Ozsváth-Szabó, including the existence of standard modules over these algebras. The authors prove that the Ext groups between standard modules are isomorphic to the homology of a variant of a certain bordered strands dg algebras.
Reviewer: Mee Seong Im (Annapolis)
MSC:
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 16G99 | Representation theory of associative rings and algebras |
| 17B15 | Representations of Lie algebras and Lie superalgebras, analytic theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 57K18 | Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) |
Keywords:
hyperplane arrangement; categorification; bordered Heegaard-Floer homology; \( \mathfrak{gl}(1 | 1)\); hypertoric varietyReferences:
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