A note on standard equivalences (Q2830652)

A finite dimensional algebra \(A\) over a field is said to be triangular if its Gabriel quiver has no oriented cycles. If \(A\) is derived equivalent to a triangular algebra, it is proved that any derived equivalence (of bounded derived categories of finitely generated modules) between \(A\) and another finite dimensional algebra is standard. This means that the equivalence is obtained by tensoring with a two-sided tilting complex. Examples of triangular algebras are piecewise hereditary ones. However, it should be noted that the triangular property is not invariant under derived equivalence.