Virtual mutations of weighted surface algebras

The finite-dimensional symmetric algebras over algebraically closed fields, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, weighted their deformations were introduced studied in [14], [15], [16], [17], [18], it was shown that all these except a few singular cases, are tame periodic period 4. this article, using general form algebra from we introduce study so called virtual mutations which constitute new large class We prove derived equivalent but not isomorphic to algebras. results paper an essential step towards classification