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	<title>Notes for AKT-091008-2/0:26:47 - Revision history</title>
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	<updated>2026-07-02T19:33:58Z</updated>
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		<id>https://drorbn.net/index.php?title=Notes_for_AKT-091008-2/0:26:47&amp;diff=8285&amp;oldid=prev</id>
		<title>Conan777 at 00:15, 21 October 2009</title>
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		<updated>2009-10-21T00:15:16Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;sketch of the proof of PBW theorem:&lt;br /&gt;
&lt;br /&gt;
Given any word, go through each letter and change the ordering of the letters by applying the relation &amp;lt;math&amp;gt;[x,y]=xy-yx&amp;lt;/math&amp;gt; this process will yield an expression of the word using only non-decreasing words in the basis elements.&lt;/div&gt;</summary>
		<author><name>Conan777</name></author>
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