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Question about Ext$^1$ in local commutative algebras

Given a local commutative (commutative only if needed...) selfinjective (non-semisimple) finite dimensional algebra $A$ over a field $K$ with enveloping algebra $A^e = A \otimes_K A^{op}$. Then $Ext_{...
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5 votes
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Ext^1 for a local finite dimensional selfinjective algebra

Is there a nonprojective module $M$ over a finite dimensional local selfinjective algebra with $Ext^{1}(M,M)=0$? I asked this question also here: http://arxiv.org/pdf/1609.00588.pdf. There it is ...
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