17 citations · 51 across the 8 of their papers we have counts for
9 papers
Frobenius algebra objects in Temperley-Lieb categories at roots of unity
Joseph Grant, Mathew Pugh
We give a new definition of a Frobenius structure on an algebra object in a monoidal category, generalising Frobenius algebras in the category of vector spaces. Our definition allo…
Mutation of signed valued quivers and presentations of simple complex Lie algebras
Joseph Grant, Davide Morigi
We introduce a signed variant of (valued) quivers and a mutation rule that generalizes the classical Fomin-Zelevinsky mutation of quivers. To any signed valued quiver we associate…
Serre functors and graded categories
Joseph Grant
We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories wit…
The Nakayama automorphism of a self-injective preprojective algebra
Joseph Grant
We give a simple proof, using Auslander-Reiten theory, that the preprojective algebra of a basic hereditary algebra of finite representation type is Frobenius. We then describe its…
Higher preprojective algebras, Koszul algebras, and superpotentials
Joseph Grant, Osamu Iyama
In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that…
Higher zigzag algebras
Joseph Grant
Given any Koszul algebra of finite global dimension one can define a new algebra, which we call a higher zigzag algebra, as a twisted trivial extension of the Koszul dual of our or…
Braid groups and quiver mutation
Joseph Grant, Bethany Marsh
We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter grou…
Lifts of longest elements to braid groups acting on derived categories
Joseph Grant
If we have a braid group acting on a derived category by spherical twists, how does a lift of the longest element of the symmetric group act? We give an answer to this question, us…
Derived autoequivalences from periodic algebras
Joseph Grant
We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction general…