On Arnold's triality theorem (Q2901333)
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scientific article; zbMATH DE number 6058397
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Arnold's triality theorem |
scientific article; zbMATH DE number 6058397 |
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19 July 2012
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Cayley-Klein geometries
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quaternions
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triality theorem
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On Arnold's triality theorem (English)
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The present paper generalizes \textit{V. I. Arnol'd}'s fundamental problem in his paper [Russ. Math. Surv. 50, No. 1, 1--68 (1995); translation from Usp. Mat. Nauk 50, No. 1, 3--68 (1995; Zbl 0848.58005)] on spherical curves and quaternion algebra, concerning the triality theorem and the nine 2-dimensional Cayley-Klein geometries. The author's approach is physically motivated, based on a work by Bacry and Levy-Leblond on possible kinematics. The paper is based on the closed relation between mechanics and mathematics, and, especially mechanics, algebra and geometry.
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