File:SO-O-PSO-PO-2k.svg
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 even dimension. |
| Date | |
| 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. |
| Author | Nils R. Barth |
See also
- File:SO-O-PSO-PO-2k+1.svg – odd dimension
- File:Spin-Pin-SO-O-definite.svg – analogous diagram for Spin & Pin groups
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}$$ % Frame for margin
\xymatrix@=6pt{
&\{\pm I\}
\ar@{^(->}@/_1pc/[ddl]
\ar@{_(->}@/^1pc/[ddr]
\\ \\
\operatorname{SO}(2k) \ar@{->>}[dd] \ar@{^(->}[rr]
&&\operatorname{O}(2k) \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]^{\det}
\\
&& &&\{\pm 1\}
\\
\operatorname{PSO}(2k) \ar@{^(->}[rr]
&&\operatorname{PO}(2k) \ar@{->>}@/_1pc/[rru]^{\det}
}
$$}}} % end math, end frame
\end{document}
Licensing
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. |