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τ-Tilting Modules Over One-Point Extensions by a Projective Module

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Abstract

Let A be the one point extension of an algebra B by a projective B-module. We prove that the extension of a given support τ-tilting B-module is a support τ-tilting A-module; and, conversely, the restriction of a given support τ-tilting A-module is a support τ-tilting B-module. Moreover, we prove that there exists a full embedding of quivers between the corresponding poset of support τ-tilting modules.

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Acknowledgments

The author thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The results of this article are part of the PhD thesis of the author under the supervision of Sonia Trepode and Claudia Chaio. She is grateful to them for their constant support and helpful discussions.

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  1. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata, 7600, Mar del Plata, Argentina

    Pamela Suarez

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  1. Pamela Suarez
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Correspondence to Pamela Suarez.

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Presented by Michel Van den Bergh.

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Suarez, P. τ-Tilting Modules Over One-Point Extensions by a Projective Module. Algebr Represent Theor 21, 769–786 (2018). https://doi.org/10.1007/s10468-017-9737-5

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