Quivers with quantum Yang-Baxter equation and Hecke condition: Deformation of face algebras

Mathematics > Quantum Algebra [Submitted on 18 Dec 2025 (v1), last revised 16 Jun 2026 (this version, v3)] Title:Quivers with quantum Yang-Baxter equation and Hecke condition: Deformation of face algebras View PDF HTML (experimental)Abstract:In this paper we initiate the study of quivers carrying quantum Yang--Baxter and Hecke structure, and we apply this framework to study path algebras over quivers whose loop spaces carry RTT relations determined by Hecke $R$-matrices. We show that the quantum matrix algebra $\mathcal{O}_q(M_n)$ is isomorphic as a bialgebra to the face algebra over a rose quiver deformed by RTT relations of the $GL_q(n)$ Hecke $R$-matrix. Submission history From: Cody Gilbert [view email][v1] Thu, 18 Dec 2025 18:05:26 UTC (150 KB) [v2] Tue, 3 Feb 2026 02:32:40 UTC (153 KB) [v3] Tue, 16 Jun 2026 16:22:36 UTC (125 KB) Current browse context: math.QA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) 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.