期刊论文详细信息
Symmetry, Integrability and Geometry: Methods and Applications | |
Erlangen Program at Large-1: Geometry of Invariants | |
关键词: analytic function theory; semisimple groups; elliptic; parabolic; hyperbolic; Clifford algebras; complex numbers; dual numbers; double numbers; split-complex numbers; Möbius transformations; | |
DOI : | |
来源: DOAJ |
【 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