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Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 4, Pages 1–7 (Mi faa267)  

This article is cited in 2 scientific papers (total in 3 papers)

Complexification of Tetrahedron and Pseudo-Projective Transformations

V. I. Arnol'dab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paris-Dauphine

Abstract: It is proved that octahedron is the complex version of tetrahedron in the following sense. The symmetry group of tetrahedron, $A_3$, can be regarded as the group of projective transformations of the space $\mathbb{R}\mathbb{P}^2$ that preserve a quadruple of points. This group can be extended to the group of transformations of the space $\mathbb{РЎ}\mathbb{P}^2$ that preserve a quadruple of points and take complex lines into complex ones. This group turns out to be the symmetry group $B_3$ of octahedron.

DOI: https://doi.org/10.4213/faa267

Full text: PDF file (108 kB)
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English version:
Functional Analysis and Its Applications, 2001, 35:4, 241–246

Bibliographic databases:

Document Type: Article
UDC: 514.144
Received: 05.07.2001

Citation: V. I. Arnol'd, “Complexification of Tetrahedron and Pseudo-Projective Transformations”, Funktsional. Anal. i Prilozhen., 35:4 (2001), 1–7; Funct. Anal. Appl., 35:4 (2001), 241–246

Citation in format AMSBIB
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\pages 241--246
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Arnol'd, “Pseudoquaternion Geometry”, Funct. Anal. Appl., 36:1 (2002), 1–12  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. G. Gorinov, “Pseudocomplex and Pseudo(bi)quaternion Mappings”, Funct. Anal. Appl., 38:2 (2004), 149–150  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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