Zobrazeno 1 - 10
of 219
pro vyhledávání: '"Grant, Joseph"'
Autor:
Grant, Joseph, Pugh, Mathew
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 allows Frobenius forms valued in objects other than the unit object, and c
Externí odkaz:
http://arxiv.org/abs/2409.12920
Autor:
Grant, Joseph, Morigi, Davide
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 a matrix that is a signed analogue of the Cartan counterpart appearing
Externí odkaz:
http://arxiv.org/abs/2403.14595
Autor:
Grant, Joseph
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 with group actions and categories with graded hom spaces. We check that S
Externí odkaz:
http://arxiv.org/abs/2007.01817
Autor:
Grant, Joseph
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 Nakayama automorphism, which is induced by the Nakayama functor on th
Externí odkaz:
http://arxiv.org/abs/1906.11817
Autor:
Grant, Joseph, Iyama, Osamu
Publikováno v:
Compositio Math. 156 (2020) 2588-2627
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 the quiver of the higher preprojective algebra is obtained by adding a
Externí odkaz:
http://arxiv.org/abs/1902.07878
Autor:
Grant, Joseph
Publikováno v:
Doc. Math. 24, 749-814 (2019)
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 original algebra. If our original algebra is the path algebra of a quive
Externí odkaz:
http://arxiv.org/abs/1711.00794
Autor:
Grant, Joseph, Marsh, Bethany
Publikováno v:
Pacific J. Math. 290 (2017) 77-116
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 groups. In types A and D these presentations can be understood geometrical
Externí odkaz:
http://arxiv.org/abs/1408.5276