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The trivial extension T(A) of a (finite dimensional) algebra A is representation-finite if and only if the algebra A is iterated tilted of Dynkin type.

Questions:

  1. Is there a similar classification when the trivial extension of an algebra is tame?

  2. Is there a classification when T(T(A)) is tame? It seems this can happens very rarely, one example is A=k, a field.

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    $\begingroup$ This at least seems to happen much more frequently: The paper "On the representation type of certain trivial extensions" by Novoa and de la Pena claims that for a tame one-point extension of a tame concealed algebra by a regular module, then its trivial extension is tame. $\endgroup$
    – Julian Kuelshammer
    Commented Mar 1, 2018 at 15:43
  • $\begingroup$ @JulianKuelshammer Thanks, Ill have a look at it. $\endgroup$
    – Mare
    Commented Mar 1, 2018 at 15:45

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