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Mare
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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. Is there a similar classification when the trivial extension of an algebra is tame? Is there a classification when T(T(A)) is tame? It seems this can happens very rarely, one example is A=k, a field.

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.

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. Is there a similar classification when the trivial extension of an algebra is tame? Is there a classification when T(T(A)) is tame? It seems this can happens very rarely, one example is A=k, a field.

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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Mare
Mare
  • 26.5k
  • 6
  • 25
  • 104

Tameness of the trivial extension of a finite dimensional algebra

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. Is there a similar classification when the trivial extension of an algebra is tame? Is there a classification when T(T(A)) is tame? It seems this can happens very rarely, one example is A=k, a field.