File:PSU-PU-2.svg

From testwiki
Jump to navigation Jump to search
    Original file (SVG file, nominally 207 × 118 pixels, file size: 24 KB)

    This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.

    Summary

    Description
    English: Commutative diagram, showing the projective special unitary group and projective unitary group, presented as (sub)quotients of the unitary group.
    Date
    Source Own work
    Author Ascchrvalstr

    Source code

    \documentclass[crop,tikz,convert={outext=.svg,command=\unexpanded{pdf2svg \infile\space\outfile}},multi=false]{standalone}
    \usepackage{tikz-cd}
    \usepackage{amsmath}
    \usepackage{amssymb}
    
    \tikzcdset{arrow style=tikz, diagrams={>=stealth}}
    
    \begin{document}
    % https://q.uiver.app/#q=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
    \begin{tikzcd}
    	{\mathbb{Z}/n} & {\operatorname{U}(1)} & {\operatorname{U}(1)} \\
    	{\operatorname{SU}(n)} & {\operatorname{U}(n)} & {\operatorname{U}(1)} \\
    	{\operatorname{PSU}(n)} & {\operatorname{PU}(n)}
    	\arrow[hook, from=1-1, to=1-2]
    	\arrow[hook, from=1-1, to=2-1]
    	\arrow["{z^n}", two heads, from=1-2, to=1-3]
    	\arrow[hook, from=1-2, to=2-2]
    	\arrow["\wr", from=1-3, to=2-3]
    	\arrow[hook, from=2-1, to=2-2]
    	\arrow[two heads, from=2-1, to=3-1]
    	\arrow["\det", two heads, from=2-2, to=2-3]
    	\arrow[two heads, from=2-2, to=3-2]
    	\arrow["\sim", from=3-1, to=3-2]
    \end{tikzcd}
    
    \end{document}
    

    Licensing

    I, the copyright holder of this work, hereby publish it under the following license:
    Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
    The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

    Captions

    Commutative diagram, showing the {{W|projective special unitary group}} and {{W|projective unitary group}}, presented as (sub)quotients of the {{W|unitary group}}.

    Items portrayed in this file

    depicts

    2 June 2026

    image/svg+xml

    File history

    Click on a date/time to view the file as it appeared at that time.

    Date/TimeThumbnailDimensionsUserComment
    current17:42, 2 June 2026Thumbnail for version as of 17:42, 2 June 2026207 × 118 (24 KB)wikimediacommons>AscchrvalstrUploaded own work with UploadWizard

    There are no pages that use this file.