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

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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 edit

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

TeX source edit

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 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.

Original upload log edit

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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