ABSTRACT
In this note we study some necessary and sufficient conditions for the one-point extension of a quasitilted algebra by an indecomposable module to be again quasitilted. In particular we show that if A is a quasitilted algebra with a convex standard stable tube T https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187759/559656af-5888-4439-a5d2-08d7a38d7161/content/inq_chapter17_177_1.tif"/> , then the one point extension by a module of the mouth of T https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187759/559656af-5888-4439-a5d2-08d7a38d7161/content/inq_chapter17_177_2.tif"/> is again quasitilted. We characterize the one-point extension of quasitilted algebras by simple modules which are quasitilted. In particular we show that in case that a tilted algebra A has a strong sink, then the one-point extension of a tilted algebra by the simple projective associated with this strong sink is always quasitilted. Finally we study the double extension of a tame hereditary algebra by indecomposable modules.
