File:SO-O-PSO-PO-2k+1.svg
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Summary[edit]
DescriptionSO-O-PSO-PO-2k+1.svg |
English: Commutative diagram connecting the special orthogonal group, orthogonal group, projective special orthogonal group, and projective orthogonal group for a definite form in odd 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. This W3C-unspecified vector image was created with Inkscape . |
Author | Nils R. Barth |
See also[edit]
- File:SO-O-PSO-PO-2k.svg – even dimension
LaTeX source[edit]
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}$$ % Frame for margin
\xymatrix@=6pt{
&&\{\pm I\}
\ar@{^(->}[dd]
\\ \\
\operatorname{SO}(2k+1) \ar[dd]^{\wr} \ar@{^(->}[rr]
&&\operatorname{O}(2k+1) \ar@{->>}[dd] \ar@{->>}[rr]^(.55){\det}
&&\{\pm 1\}
\\
\\
\operatorname{PSO}(2k+1) \ar[rr]^{=}
&&\operatorname{PO}(2k+1)
}
$$}}} % 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 domainPublic domainfalsefalse |
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. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:47, 8 May 2010 | 466 × 211 (43 KB) | Nbarth (talk | contribs) | {{Information |Description = {{en|Commutative diagram connecting the special orthogonal group, orthogonal group, projective special orthogonal group, and |
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