Erlangen Program at Large-1: Geometry of Invariants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• ISSN: 1815-0659
• Main Author: Kisil, V.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146514
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Erlangen Program at Large-1: Geometry of Invariants / V.V. Kisil // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 73 назв. — англ.

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 rôle is played by Cliff...