Hilbert-Samuel Polynomials for Algebras with Special Filtrations

[2407.21166] Hilbert-Samuel Polynomials for Algebras with Special Filtrations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Rings and Algebras arXiv:2407.21166 (math) [Submitted on 30 Jul 2024] Title: Hilbert-Samuel Polynomials for Algebras with Special Filtrations Authors: Jonas T. Hartwig , Erich C. Jauch , João Schwarz View a PDF of the paper titled Hilbert-Samuel Polynomials for Algebras with Special Filtrations, by Jonas T. Hartwig and 2 other authors View PDF HTML (experimental) Abstract: The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials. For noncommutative rings, the notion of multiplicity first appeared in the context of modules for the Weyl algebra in Bernstein's solution of the problem of analytic continuation posed by I. Gelfand. The notion was shown to be useful to many more noncommutative rings, especially enveloping algebras, rings of differential operators, and quantum groups. In all these cases, the existence of multiplicity is related to the existence of Hilbert-Samuel polynomials. In this work we give an axiomatic definition of algebras with a notion of multiplicity, which we call very nice and modest algebras. We show, in an abstract setting, how the existence of Hilbert-Samuel polynomials implies the existence of a notion of multiplicity. We apply our results for the category of min-holonomic modules -- a notion which coincides with holonomic modules for simple algebras -- and that shares many similarities with it. In particular, we generalize the usual results in the literature that are stated for Ore domains, in the more general context of prime algebras, and we show that rational Cherednik algebras admit a notion of multiplicity. Comments: 26 pages Subjects: Rings and Algebras (math.RA) MSC classes: 16P90 (Primary) Cite as: arXiv:2407.21166 [math.RA] (or arXiv:2407.21166v1 [math.RA] for this version) https://doi.org/10.48550/arXiv.2407.21166 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1142/S0219498827500344 Focus to learn more DOI(s) linking to related resources Submission history From: Erich Jauch [ view email ] [v1] Tue, 30 Jul 2024 20:11:52 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled Hilbert-Samuel Polynomials for Algebras with Special Filtrations, by Jonas T. Hartwig and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.RA < prev | next > new | recent | 2024-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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

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