File:Spin-Pin-SO-O-definite.svg
Summary
| 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
- File:SO-O-PSO-PO-2k.svg – analogous diagram for projective (special) orthogonal group in even dimension (PSO(2k) and PO(2k))
TeX source
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
Nils R. Barth, the copyright holder of this work, hereby publishes it under the following license:
 |
This work has been released into the public domain by its author, Nils R. Barth. This applies worldwide. In some countries this may not be legally possible; if so: Nils R. Barth grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
Original upload log
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.