Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 56: Issue 1
Revisiting the universal linear algebraic model for the characteristic two case
Author:
Máté L. Juhász Eszterházy Károly University, HU-3300, Eger, Leányka út 4., C

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Pages:
81–93
Online Publication Date:
Mar 2019
Publication Date:
01 Mar 2019
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2019.56.1.1411
Keywords:
characteristic 2; conformal geometry; quadratic spaces; orthogonal groups
Open access

Abstract

In [3], a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes ([6]). This formalism was independent from the underlying field, providing an extension and general approach to other fields, such as finite fields. Some steps were taken even for the characteristic 2 case.

In this article, we undertake the study of the characteristic 2 case in more detail. In particular, the concept of virtual quadratic spaces is used ([4]), and a similar result is achieved for finite fields of characteristic 2 as for other fields. Some differences from the non-characteristic 2 case are also pointed out.

  • [1]

    Baeza, R. and Moresi, R., On the Witt-Equivalence of Fields of Characteristic 2, Journal of Algebra. 92 (1985) 446–453.

  • [2]

    Hestens, D., Hestens, Li., Hestens, H. and Rockwood, A., A unified algebraic framework for classical geometry, 2000. http://geocalc.clas.asu.edu/html/UAFCG.html

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  • [3]

    Juhász, M., Juhász, L., A universal linear algebraic model for conformal geometries, Journal of Geometry, 109:48 (2018), https://doi.org/10.1007/s00022-018-0451-1.

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  • [4]

    Juhász, M., Juhász, L., Isometries of virtual quadratic spaces, Annales Univ. Sci. Sect. Math., 59 (2016), 123–132. arXiv:1612.02682

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  • [5]

    Kitaoka, Y. , Arithmetic of quadratic forms, Cambridge University Press, 1993.

  • [6]

    Yaglom, I. M. , Galilei's Relativity Principle and Non-Euclidean Geometry, Nauka, 1969.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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