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Universal localisations and tilting modules for finite dimensional algebras (1307.6496v1)

Published 24 Jul 2013 in math.RT and math.RA

Abstract: 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 $\tau$-tilting modules, which were recently introduced by Adachi, Iyama and Reiten.

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