ABSTRACT
In [4], Bautista and Martínez introduced what we will call the ”double extension” algebra Λ ^ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187759/559656af-5888-4439-a5d2-08d7a38d7161/content/inq_chapter15_157_1.tif"/> of a finite poset S. We will denote by Λ the incidence algebra of S. The tilted algebras were introduced by Happel and Ringel in [5] and since then, have been proven to be a powerful tool in the study of different classes of algebras. The main result of this paper is a theorem that relates the property of Λ ^ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187759/559656af-5888-4439-a5d2-08d7a38d7161/content/inq_chapter15_157_2.tif"/> being tilted to the same condition in Λ. Some corollaries give more precise results in the cases: Λ is hereditary, Λ is tilted, Λ is tilted and of finite representation type.
