Resumen de Universal localisations and tilting modules for finite dimensional algebras

Frederik Marks

• We study universal localisations, in the sense of Cohn and Schofield, for finite dimensional algebras and classify them by certain subcategories of our initial module category. A complete classification is presented in the hereditary case as well as for Nakayama algebras and local algebras. Furthermore, for hereditary algebras, we establish a correspondence between finite dimensional universal localisations and finitely generated support tilting modules. In the Nakayama case, we get a similar result using τ-tilting modules, which were recently introduced by Adachi, Iyama and Reiten.