Extension dimension of the i-th syzygy module category is invariant under derived equivalence for large i and under stable/separable equivalence for all nonnegative i.
Derived dimensions of representation-finite algebras
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It is shown that the derived dimension of any representation-finite Artin algebra is at most one.
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The Extension dimension of syzygy module categories
Extension dimension of the i-th syzygy module category is invariant under derived equivalence for large i and under stable/separable equivalence for all nonnegative i.