تقرير
Erlangen Program at Large: Outline
| العنوان: | Erlangen Program at Large: Outline |
|---|---|
| المؤلفون: | Kisil, Vladimir V. |
| سنة النشر: | 2010 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematics - Functional Analysis, Mathematics - Metric Geometry, 30G35, 22E46, 30F45, 32F45, 43A85, 30G30, 42C40, 46H30, 47A13, 81R30, 81R60 |
| الوصف: | 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, M\"obius transformations, functional calculus, spectrum, quantum mechanics, non-commutative geometry. Comment: 21 pages, AMSLaTeX, 22 PS graphics files in 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1006.2115 |
| رقم الأكسشن: | edsarx.1006.2115 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |