Erlangen Program at Large--2: Inventing a wheel. The parabolic one

Vladimir V. Kisil

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arXiv · 0707.4024

Erlangen Program at Large--2: Inventing a wheel. The parabolic one

Vladimir V. Kisil

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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

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Vladimir V. Kisil. 2007-07-27. Erlangen Program at Large--2: Inventing a wheel. The parabolic one. https://arxiv.org/abs/0707.4024

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