File:Hopf algebra.svg

Original file (SVG file, nominally 185 × 166 pixels, file size: 30 KB)

Summary

Description
English: A commutative hexagon expressing all the axioms of a Hopf algebra.
Date
Source Own work
Author Ryan Reich
Other versions File:HopfAlgebra.png

Source code

\documentclass{article} \usepackage{amsmath,amssymb,nopageno} \usepackage[all]{xy} \DeclareMathOperator{\id}{id} \begin{document}  \begin{equation*}   \[email protected]@R+2em{   & {H \otimes H} \ar[rr]^{S \otimes \id} & & {H \otimes H} \ar[dr]^{\nabla} & \\   {H} \ar[ur]^{\Delta} \ar[dr]_{\Delta} \ar[rr]^{\varepsilon} & & {K} \ar[rr]^{\eta} & & {H} \\   & {H \otimes H} \ar[rr]_{\id \otimes S} & & {H \otimes H} \ar[ur]_{\nabla} &   }  \end{equation*} \end{document} 

Licensing

Public domain 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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

29 April 2009

image/svg+xml

File history

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

Date/TimeThumbnailDimensionsUserComment
current19:58, 29 April 2009Thumbnail for version as of 19:58, 29 April 2009185 × 166 (30 KB)Ryan Reich{{Information |Description={{en|1=A commutative hexagon expressing all the axioms of a Hopf algebra.}} |Source=Own work by uploader |Author=Ryan Reich |Date=2009-04-29 |Permission= |other_versions=File:HopfAlgebra.png }} == Source

The following 2 pages use this file:

Global file usage

The following other wikis use this file: