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We derive an algorithm for mutating quivers of 2-CY tilted algebras that haveloops and 2-cycles, under certain specific conditions. Further, we give theclassification of the 2-CY tilted algebras coming from standard algebraic 2-CYtriangulated categories with a finite number of indecomposables. These form aclass of algebras that satisfy the setup for our mutation algorithm.

Mutating loops and 2-cycles in 2-CY triangulated categories