Strands algebras and the affine highest weight property for equivariant hypertoric categories

TL;DR

This paper demonstrates that equivariant hypertoric convolution algebras are affine quasi hereditary, computes Ext groups between standard modules, and links these algebraic structures to bordered Floer homology, revealing new homological insights.

Contribution

It establishes the affine quasi hereditary property for equivariant hypertoric convolution algebras and connects Ext groups to bordered strands dg algebra homology, advancing homological understanding.

Findings

Equivariant hypertoric convolution algebras are affine quasi hereditary.

Ext groups between standard modules are computed and related to bordered algebra homology.

New homological results for bordered Floer algebras are derived.

Abstract

We show that the equivariant hypertoric convolution algebras introduced by Braden-Licata-Proudfoot-Webster are affine quasi hereditary in the sense of Kleshchev and compute the Ext groups between standard modules. Together with the main result of arXiv:2009.03981, this implies a number of new homological results about the bordered Floer algebras of Ozsvath-Szabo, including the existence of standard modules over these algebras. We prove that the Ext groups between standard modules are isomorphic to the homology of a variant of the Lipshitz-Ozsvath-Thurston bordered strands dg algebras.