Erlangen Program at Large--2: Inventing a wheel. The parabolic one
General Mathematics
2010-11-25 v1 Rings and Algebras
Representation Theory
Abstract
We discuss parabolic versions of Euler's identity e^{it}=cos t + i sin t. A purely algebraic approach based on dual numbers is known to produce a very trivial relation e^{pt} = 1+pt. Therefore we use a geometric setup of parabolic rotations to recover the corresponding non-trivial algebraic framework. Our main tool is Moebius transformations which turn out to be closely related to induced representations of the group SL(2,R). Keywords: complex numbers, dual numbers, double numbers, linear algebra, invariant, computer algebra, GiNaC
Cite
@article{arxiv.0707.4024,
title = {Erlangen Program at Large--2: Inventing a wheel. The parabolic one},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:0707.4024},
year = {2010}
}
Comments
LaTeX paper (14 pages) and software documentation in an appendix (20 pages); two figures (five PS files)