A complete derived invariant and silting theory for graded gentle algebras

H Jin, S Schroll, Z Wang - arXiv preprint arXiv:2303.17474, 2023 - arxiv.org
We show that among the derived equivalent classes of homologically smooth and proper
graded gentle algebras there is only one class whose perfect derived category does not …

On support τ-tilting graphs of gentle algebras

C Fu, S Geng, P Liu, Y Zhou - Journal of Algebra, 2023 - Elsevier
Let A be a finite-dimensional gentle algebra over an algebraically closed field. We
investigate the combinatorial properties of support τ-tilting graph of A. In particular, it is …

Exceptional sequences in the derived category of a gentle algebra

W Chang, S Schroll - Selecta Mathematica, 2023 - Springer
In this paper, using the correspondence of gentle algebras and dissections of marked
surfaces, we study full exceptional sequences in the perfect derived category K b (A) of a …

Generalized Kauer moves and derived equivalences of Brauer graph algebras

V Soto - Journal of Algebra, 2024 - Elsevier
Kauer moves are local moves of an edge in a Brauer graph that yield derived equivalences
between Brauer graph algebras [10]. These derived equivalences may be interpreted in …

Recollements of partially wrapped Fukaya categories and surface cuts

W Chang, H Jin, S Schroll - arXiv preprint arXiv:2206.11196, 2022 - arxiv.org
In this paper we use recollements to investigate partially wrapped Fukaya categories of
surfaces with marked points. In particular, we show that cutting surfaces gives rise to …

Skew-group A∞-categories as Fukaya categories of orbifolds

C Amiot, PG Plamondon - 2024 - cnrs.hal.science
We study the partially wrapped Fukaya category of a surface with boundary with an action of
a group of order two. Inspired by skew-group algebras and categories, we define the notion …

Triangulations of Prisms and Preprojective Algebras of Type A

O Iyama, NJ Williams - International Mathematics Research …, 2024 - academic.oup.com
We show that isomorphism classes of indecomposable-rigid pairs over, the preprojective
algebra of, are in bijection with internal-simplices in the prism, the product of an-simplex with …

A geometric model for the module category of a string algebra

K Baur, RC Simoes - arXiv preprint arXiv:2403.07810, 2024 - arxiv.org
In this paper, we give a geometric construction of string algebras and of their module
categories. Our approach uses dissections of punctured Riemann surfaces with extra data at …

Derived discrete Hopf algebras with the Chevalley property

J Yu, G Liu - arXiv preprint arXiv:2412.08093, 2024 - arxiv.org
We try to classify Hopf algebras with the Chevalley property according to their derived
representation type. We show that a finite-dimensional indecomposable non-semisimple …

Skew-group -categories as Fukaya categories of orbifolds

C Amiot, PG Plamondon - arXiv preprint arXiv:2405.15466, 2024 - arxiv.org
We study the partially wrapped Fukaya category of a surface with boundary with an action of
a group of order two. Inspired by skew-group algebras and categories, we define the notion …