Lectures on Representations of Quivers by William Crawley-Boevey ...
Lectures on Representations of Quivers by William Crawley-Boevey ...
Lectures on Representations of Quivers by William Crawley-Boevey ...
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PROOF. By assumpti<strong>on</strong> 0 = ( ,¥ ) = (2-2n )¥ - ¤ n ¥ .<br />
i ii i j£ i ij j<br />
If ¥ =0 then ¤ n ¥ = 0, and since each term in £ 0 we have ¥ =0<br />
i j£ i ij j j<br />
whenever there is an edge i j. Since is c<strong>on</strong>nected it follows that ¥ =0, a<br />
c<strong>on</strong>tradicti<strong>on</strong>. Thus ¥ is sincere. Now<br />
i j©<br />
¤ j i<br />
n -<br />
i