The \(k\)-Cauchy-Fueter complex, Penrose transformation and hartogs phenomenon for quaternionic \(k\)-regular functions

DOI10.1016/j.geomphys.2009.11.011zbMath1184.30050OpenAlexW1965476687MaRDI QIDQ2268979

Wei Wang

Publication date: 15 March 2010

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2009.11.011

zbMATH Keywords

\(k\)-Cauchy-Fueter complexPenrose transformationquaternionic \(k\)-regular functions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Twistor theory, double fibrations (complex-analytic aspects) (32L25) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Differential complexes (58J10) Overdetermined systems of PDEs with constant coefficients (35N05)

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Cites Work

• Explicit resolutions for the complex of several Fueter operators
• On non-homogeneous Cauchy-Fueter equations and Hartogs' phenomenon in several quaternionic variables
• Regular functions of several quaternionic variables
• Cohomology and massless fields
• Quaternionic complexes
• Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
• Regular functions of several quaternionic variables and the Cauchy-Fueter complex
• Analysis of Dirac systems and computational algebra.
• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables.
• Invariant resolutions for several Fueter operators
• Complex manifolds and mathematical physics
• Analysis of the module determining the properties of regular functions of several quaternionic variables.
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