---
_id: '63135'
abstract:
- lang: eng
  text: We propose a definition of Coxeter-Dynkin algebras of canonical type generalising
    the definition as a path algebra of a quiver. Moreover, we construct two tilting
    objects over the squid algebra - one via generalised APR-tilting and one via one-point-extensions
    and reflection functors - and identify their endomorphism algebras with the Coxeter-Dynkin
    algebra. This shows that our definition gives another representative in the derived
    equivalence class of the squid algebra, and hence of the corresponding canonical
    algebra. Finally, we have a closer look at the Grothendieck group and the Euler
    form which illustrates the connection to Saito's classification of marked extended
    affine root systems. On the other hand, this enables us to prove that in the domestic
    case Coxeter-Dynkin algebras are of finite representation type.
author:
- first_name: Daniel
  full_name: Perniok, Daniel
  id: '64242'
  last_name: Perniok
citation:
  ama: Perniok D. Coxeter-Dynkin algebras of canonical type. <i>Journal of Pure and
    Applied Algebra</i>. 2026;230(5). doi:<a href="https://doi.org/10.1016/j.jpaa.2026.108250">10.1016/j.jpaa.2026.108250</a>
  apa: Perniok, D. (2026). Coxeter-Dynkin algebras of canonical type. <i>Journal of
    Pure and Applied Algebra</i>, <i>230</i>(5). <a href="https://doi.org/10.1016/j.jpaa.2026.108250">https://doi.org/10.1016/j.jpaa.2026.108250</a>
  bibtex: '@article{Perniok_2026, title={Coxeter-Dynkin algebras of canonical type},
    volume={230}, DOI={<a href="https://doi.org/10.1016/j.jpaa.2026.108250">10.1016/j.jpaa.2026.108250</a>},
    number={5}, journal={Journal of Pure and Applied Algebra}, author={Perniok, Daniel},
    year={2026} }'
  chicago: Perniok, Daniel. “Coxeter-Dynkin Algebras of Canonical Type.” <i>Journal
    of Pure and Applied Algebra</i> 230, no. 5 (2026). <a href="https://doi.org/10.1016/j.jpaa.2026.108250">https://doi.org/10.1016/j.jpaa.2026.108250</a>.
  ieee: 'D. Perniok, “Coxeter-Dynkin algebras of canonical type,” <i>Journal of Pure
    and Applied Algebra</i>, vol. 230, no. 5, 2026, doi: <a href="https://doi.org/10.1016/j.jpaa.2026.108250">10.1016/j.jpaa.2026.108250</a>.'
  mla: Perniok, Daniel. “Coxeter-Dynkin Algebras of Canonical Type.” <i>Journal of
    Pure and Applied Algebra</i>, vol. 230, no. 5, 2026, doi:<a href="https://doi.org/10.1016/j.jpaa.2026.108250">10.1016/j.jpaa.2026.108250</a>.
  short: D. Perniok, Journal of Pure and Applied Algebra 230 (2026).
date_created: 2025-12-16T14:20:09Z
date_updated: 2026-04-23T13:00:59Z
department:
- _id: '602'
doi: 10.1016/j.jpaa.2026.108250
external_id:
  arxiv:
  - '2509.17887'
intvolume: '       230'
issue: '5'
language:
- iso: eng
publication: Journal of Pure and Applied Algebra
status: public
title: Coxeter-Dynkin algebras of canonical type
type: journal_article
user_id: '64242'
volume: 230
year: '2026'
...