2010/06/10 by Vladimir V. Kisil, Kisil, Vladimir V.
Mathematics · #22E46 #30F45 #30G30 #30G35 #32F45 #42C40 #43A85 #46H30 #47A13 #81R30 #81R60 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Metric Geometry (math.MG) #math.CV #math.FA #math.MG #msc:22E46 #msc:30F45 #msc:30G30 #msc:30G35 #msc:32F45 #msc:42C40 #msc:43A85 #msc:46H30 #msc:47A13 #msc:81R30 #msc:81R60
paper · pdf · doi:10.48550/arxiv.1006.2115
21 pages, AMSLaTeX, 22 PS graphics files in 8 figures
arxiv created 2010/06/10 · openalex publication_date 2010/06/10 · arxiv updated 2010/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an outline of Erlangen Program at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group SL(2,R). Starting from the conformal geometry we develop analytic functions and apply these to functional calculus. Finally we provide an extensive description of open problems. Keywords: Special linear group, Hardy space, Clifford algebra, elliptic, parabolic, hyperbolic, complex numbers, dual numbers, double numbers, split-complex numbers, Cauchy-Riemann-Dirac operator, Möbius transformations, functional calculus, spectrum, quantum mechanics, non-commutative geometry.