Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case

Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case Chen Liang, Matvei Libine This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3301458/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Apr, 2024 Read the published version in Complex Analysis and Operator Theory → Version 1 posted 2 You are reading this latest preprint version Abstract We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions -- called monogenic functions -- are defined by means of the Dirac operators that factor a certain wave operator. One of the fundamental features of quaternionic analysis is the invariance of quaternionic analogues of holomorphic function under conformal (or Mobius) transformations. A similar invariance property is known to hold in the context of Clifford algebras associated to positive definite quadratic forms. We generalize these results to the case of Clifford algebras associated to all non-degenerate quadratic forms. This result puts the indefinite signature case on the same footing as the classical positive definite case. conformal transformations on ℝp q Möbius transformations Vahlen matrices monogenic functions Clifford analysis Clifford algebras conformal compactification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Apr, 2024 Read the published version in Complex Analysis and Operator Theory → Version 1 posted Submission checks completed at journal 29 Aug, 2023 First submitted to journal 27 Aug, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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