Kisil, VV orcid.org/0000-0002-6593-6147 (2010) Erlangen Program at Large-1: Geometry of Invariants. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 6 (76).
Abstract
This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL2 (R) group. We describe here geometries of corresponding domains. The principal rˆole is played by Clif ford algebras of matching types. In this paper we also generalise the Fillmore–Springer–Cnops construction which describes cycles as points in the extended space. This allows to consider many algebraic and geometric invariants of cycles within the Erlangen program approach.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | analytic function theory; semisimple groups; elliptic; parabolic; hyperbolic; Clif ford algebras; complex numbers; dual numbers; double numbers; split-complex numbers; Möbius transformations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Jul 2019 08:10 |
Last Modified: | 16 Jul 2019 08:10 |
Status: | Published |
Identification Number: | 10.3842/SIGMA.2010.076 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111538 |