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File:SO-O-PSO-PO-2k+1.svg

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Original file (SVG file, nominally 466 × 211 pixels, file size: 43 KB)

Summary

Description
English: Commutative diagram connecting the special orthogonal group, orthogonal group, projective special orthogonal group, and projective orthogonal group for a definite form in odd dimension.
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Source

Own work

Created as per: en:meta:Help:Displaying a formula#Commutative diagrams; source code below. Resized using Inkscape and manually edition of the SVG.

 
This W3C-unspecified vector image was created with Inkscape .
Author Nils R. Barth

See also

LaTeX source

Created as per: en:meta:Help:Displaying a formula#Commutative diagrams.

\documentclass{amsart}
\usepackage[all, ps]{xy} % Loading the XY-Pic package
                         % Using postscript driver for smoother curves
\usepackage{color}       % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix@=6pt{ 
&&\{\pm I\}
  \ar@{^(->}[dd]
\\ \\
   \operatorname{SO}(2k+1)   \ar[dd]^{\wr}  \ar@{^(->}[rr]
 &&\operatorname{O}(2k+1)    \ar@{->>}[dd]  \ar@{->>}[rr]^(.55){\det}
 &&\{\pm 1\}
\\
\\
   \operatorname{PSO}(2k+1)  \ar[rr]^{=}
 &&\operatorname{PO}(2k+1)
}

$$}}} % end math, end frame
\end{document}

Licensing

Nils R. Barth, the copyright holder of this work, hereby publishes it under the following license:
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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7 May 2010

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Date/TimeThumbnailDimensionsUserComment
current17:47, 8 May 2010Thumbnail for version as of 17:47, 8 May 2010466 × 211 (43 KB)Nbarth{{Information |Description = {{en|Commutative diagram connecting the special orthogonal group, orthogonal group, projective special orthogonal group, and

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