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 modulesMathematics Subject Classification (2010)
16G20 16E10 16E30Preview
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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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