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Given a finite dimensional (non-selfinjective) algebra $A$.

Is there a method (for example using QPA) to construct algebras stable equivalent to $A$?

Such a thing is easily possible for derived equivalences via tilting modules but I have not seen such a method for stable equivalences (that do not come necessarily from derived equivalences).

Special cases such as Nakayama algebras are also welcome. In particular:

Is it known when two Nakayama algebras are stable equivalent? If not, can this be tested with QPA?

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    $\begingroup$ How do you easily find a tilting module over an arbitrary finite dimensional algebra? I assume that then it is similarly easy to at least construct stable equivalences of Morita type. $\endgroup$
    – Julian Kuelshammer
    Commented Jun 5, 2019 at 14:20
  • $\begingroup$ @JulianKuelshammer At least for most algebras it is possible with QPA. For representation-finite algebras QPA can find all tilting modules. $\endgroup$
    – Mare
    Commented Jun 5, 2019 at 14:27
  • $\begingroup$ What is the expanded mame of QPA? $\endgroup$
    – Marco Farinati
    Commented Jun 6, 2019 at 0:50
  • $\begingroup$ @MarcoFarinati See folk.ntnu.no/oyvinso/QPA for the name and more information. $\endgroup$
    – Mare
    Commented Jun 6, 2019 at 7:16
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    $\begingroup$ @Mare, thanks for the link saying "Quiver Path Algebras" $\endgroup$
    – Marco Farinati
    Commented Jun 6, 2019 at 19:02

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