Construction of Milnorian representations

[1802.07193] Construction of Milnorian representations Skip to main content Search Submit Donate Log in Mathematics > Group Theory arXiv:1802.07193 (math) [Submitted on 20 Feb 2018 ( v1 ), last revised 28 Jun 2019 (this version, v2)] Title: Construction of Milnorian representations Authors: Ilia Smilga View PDF HTML (experimental) Abstract: We prove a partial converse to the main theorem of the author's previous paper "Proper affine actions: a sufficient criterion" (submitted; available at arXiv:1612.08942 ). More precisely, let $G$ be a semisimple real Lie group with a representation $\rho$ on a finite-dimensional real vector space $V$, that does not satisfy the criterion from the previous paper. Assuming that $\rho$ is irreducible and under some additional assumptions on $G$ and $\rho$, we then prove that there does not exist a group of affine transformations acting properly discontinuously on $V$ whose linear part is Zariski-dense in $\rho(G)$. Comments: This version differs from the previous one only by a reference that I added Subjects: Group Theory (math.GR) ; Representation Theory (math.RT) MSC classes: 20G20, 20G05, 22E40, 20H15 Cite as: arXiv:1802.07193 [math.GR] (or arXiv:1802.07193v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.1802.07193 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s10711-019-00476-8 Focus to learn more DOI(s) linking to related resources Submission history From: Ilia Smilga [ view email ] [v1] Tue, 20 Feb 2018 16:37:47 UTC (20 KB) [v2] Fri, 28 Jun 2019 13:33:02 UTC (20 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2018-02 Change to browse by: math math.RT 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)

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