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

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Original file ‎(SVG file, nominally 437 × 236 pixels, file size: 228 KB)

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

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LaTeX source[edit]

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@{^(->}@/_1pc/[ddl]
  \ar@{_(->}@/^1pc/[ddr]
\\ \\
   \operatorname{SO}(2k) \ar@{->>}[dd] \ar@{^(->}[rr]
 &&\operatorname{O}(2k)  \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]^{\det}
\\
 &&                                                             &&\{\pm 1\}
\\
   \operatorname{PSO}(2k)              \ar@{^(->}[rr]
 &&\operatorname{PO}(2k)               \ar@{->>}@/_1pc/[rru]^{\det}
}

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

Licensing[edit]

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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current17:44, 8 May 2010Thumbnail for version as of 17:44, 8 May 2010437 × 236 (228 KB)Nbarth (talk | contribs){{Information |Description = {{en|Commutative diagram connecting the special orthogonal group, orthogonal group, projective special orthogonal group, and

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