File:Spin-Pin-SO-O-definite.svg

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Original file ‎(SVG file, nominally 434 × 240 pixels, file size: 39 KB)

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Summary

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Description
English: Commutative diagram connecting the spin group, pin group, special orthogonal group, and orthogonal group, for a definite form.
Date 28 November 2007 (original upload date)
Source Own work by Nils R. Barth.
Author Nils R. Barth

See also

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  • File:SO-O-PSO-PO-2k.svg – analogous diagram for projective (special) orthogonal group in even dimension (PSO(2k) and PO(2k))

TeX source

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TeX source, produced as detailed at 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 1\}
  \ar@{^(->}@/_1pc/[ddl]
  \ar@{_(->}@/^1pc/[ddr]
\\ \\
   \operatorname{Spin}(n)     \ar@{->>}[dd] \ar@{^(->}[rr]
 &&\operatorname{Pin}_\pm(n)  \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]^{D}
\\
 &&                                                             &&\{\pm 1\}
\\
   \operatorname{SO}(n)                     \ar@{^(->}[rr]
 &&\operatorname{O}(n)                      \ar@{->>}@/_1pc/[rru]^{\det}
}

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

Licensing

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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.

Original upload log

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Transferred from en.wikipedia to Commons by Nbarth using CommonsHelper.

The original description page was here. All following user names refer to en.wikipedia.
  • 2007-11-28 00:07 Nbarth 434×240× (40158 bytes) Commutative diagram connecting spin group, pin group, special orthogonal group, and orthogonal group, for a definite form.

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Date/TimeThumbnailDimensionsUserComment
current17:58, 7 May 2009Thumbnail for version as of 17:58, 7 May 2009434 × 240 (39 KB)File Upload Bot (Magnus Manske) (talk | contribs) {{BotMoveToCommons|en.wikipedia|year={{subst:CURRENTYEAR}}|month={{subst:CURRENTMONTHNAME}}|day={{subst:CURRENTDAY}}}} {{Information |Description={{en|Commutative diagram connecting spin group, pin group, special orthogonal group, and orthogonal group, f

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