Erlangen Program at Large-1: Geometry of Invariants

Symmetry Integrability and Geometry-Methods and Applications

article

Vladimir V. Kisil¹ 

[1] School of Mathematics, University of Leeds

关键词: analytic function theory;    semisimple groups;    elliptic;    parabolic;    hyperbolic;    Clif ford algebras;    complex numbers;    dual numbers;    double numbers;    split-complex numbers;    M¨obius transformations;   

DOI  :  10.3842/SIGMA.2010.076

来源: National Academy of Science of Ukraine

【 摘 要 】

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 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.

【 授权许可】

Unknown