Coxeter-Dynkin algebras of canonical type

[2509.17887] Coxeter-Dynkin algebras of canonical type Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2509.17887 (math) [Submitted on 22 Sep 2025 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Coxeter-Dynkin algebras of canonical type Authors: Daniel Perniok View PDF HTML (experimental) Abstract: 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. Comments: Typos corrected, Remark 1.8 added Subjects: Representation Theory (math.RT) MSC classes: 16G10, 16E35, 16G60 Cite as: arXiv:2509.17887 [math.RT] (or arXiv:2509.17887v3 [math.RT] for this version) https://doi.org/10.48550/arXiv.2509.17887 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Pure Appl. Algebra 230 (2026), no. 5, Paper No. 108250 Related DOI : https://doi.org/10.1016/j.jpaa.2026.108250 Focus to learn more DOI(s) linking to related resources Submission history From: Daniel Perniok [ view email ] [v1] Mon, 22 Sep 2025 15:18:57 UTC (30 KB) [v2] Tue, 2 Dec 2025 10:52:26 UTC (34 KB) [v3] Thu, 27 Aug 2026 08:28:53 UTC (34 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2025-09 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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