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Algebras and Representation Theory

, Volume 21, Issue 4, pp 769–786 | Cite as

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.

Keywords

One-point extension Tilting modules Poset τ-tilting modules 

Mathematics Subject Classification (2010)

16G20 16E10 16E30 

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Notes

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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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Funes 3350Universidad Nacional de Mar del PlataMar del PlataArgentina

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