File:PSL-PGL.svg
Summary
| Description |
English: Commutative diagram showing the projective linear groups (special and general) and their relations |
| Date | |
| Source | Own work, created as per: en:meta:Help:Displaying a formula#Commutative diagrams; source code below. |
| Author | Nils R. Barth |
LaTeX source
\documentclass{amsart}
\usepackage[all, ps, dvips]{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}$$ % Frame for margin
\xymatrix{
\mathrm{SZ}(V) \ar@{^(->}[r] \ar@{^(->}[d]
& \mathrm{Z}(V)\cong F^* \ar@{->>}[r]^(.6){\det \cong z^n} \ar@{^(->}[d]
& (F^*)^n \ar@{^(->}[d] \\
\mathrm{SL}(V) \ar@{^(->}[r] \ar@{->>}[d]
& \mathrm{GL}(V) \ar@{->>}[r]^{\det} \ar@{->>}[d]
& F^* \ar@{->>}[d] \\
\mathrm{PSL}(V) \ar@{^(->}[r]
& \mathrm{PGL}(V) \ar@{->>}[r]
& F^*/(F^*)^n
}
$$}}} % 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. |
