Erlangen Program at Large-1: Geometry of Invariants

Vladimir V. Kisil

Type: Article

Publication Date: 2010-09-26

Citations: 22

DOI: https://doi.org/10.3842/sigma.2010.076

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 SL 2 (R) group.We describe here geometries of corresponding domains.The principal rôle is played by Clifford algebras of matching types.In this paper we also generalise the Schwerdtfeger-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.

Locations

Symmetry Integrability and Geometry Methods and Applications - View - PDF
arXiv (Cornell University) - View - PDF
The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine) - View - PDF
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