Higher Homological Algebra and Fractional Calabi-Yau Algebras

Haden, Jordan (2026) Higher Homological Algebra and Fractional Calabi-Yau Algebras. Doctoral thesis, University of East Anglia.

Preview

PDF Download (789kB) | Preview

Abstract

In Part I, we present a family of selfinjective algebras of type D, which are Morita equivalent to skew group algebras of the 3-preprojective algebras of type A. One-in-three is itself a 3-preprojective algebra, and the corresponding 2-representation-finite algebras are fractional Calabi-Yau. We show that our work is connected to modular invariants for SU(3), and give recipes to construct 2-Auslander-Reiten quivers for an arbitrary 2-representation-finite algebra.

In Part II, we reinterpret Thomas’ construction of a Bridgeland stability condition on the dg perfect derived category of a classical zigzag algebra of type A, explaining why the family of stable objects takes the form it does. Our attempts to generalise this construction to higher zigzag algebras of type A fail, but we are able to prove a certain group acts by spherical twists in this case. We also study a connection between tilting hearts of t-structures and mutating quivers with potentials.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Depositing User:	Chris White
Date Deposited:	13 Apr 2026 07:43
Last Modified:	13 Apr 2026 07:43
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102756
DOI:

Downloads

Actions (login required)

View Item