We shall show that every stable equivalence (functor) between representation-finite selfinjective algebras not of type (D 3m , s/3, 1) with m ≥ 2, 3 s lifts to a standard derived equivalence. This implies that all stable equivalences between these algebras are of Morita type.
In this work, we propose a new invariant for 2D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In addition, we propose an "interval-decomposable approximation" δ * (M ) of a 2D persistence module M . In the case that M is interval-decomposable, we show that δ * (M ) = M . Furthermore, even for representations M not necessarily interval-decomposable, δ * (M ) preserves the dimension vector and the rank invariant of M .
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