Notes for AKT-091008-2/0:26:47
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sketch of the proof of PBW theorem:
Given any word, go through each letter and change the ordering of the letters by applying the relation this process will yield an expression of the word using only non-decreasing words in the basis elements.
![{\displaystyle [x,y]=xy-yx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42b4220c8122ebd2a21c517ca80639581679cfa6)
