Erlangen Program at Large-1: Geometry of Invariants

Details Erlangen Program at Large-1: Geometry of Invariants Erlangen Program at Large-1: Geometry of Invariants

2005-12-17

arxiv.org/abs/math/0512416v10

SIGMA 6 (2010), 076, 45 pages

Mathematics

Complex Variables

AMS-LaTeX, 45 p, 80 PS graphics in 19 figures; v2: a reference corrected; v3: a substantial revision of the entire paper; v4:

Scientific paper

10.3842/SIGMA.2010.076

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 role 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. For an easy-reading introduction see arXiv:math/0607387. An outline of the whole approach is given in arXiv:1006.2115.

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