$\tau$-tilting modules over one-point extensions by a projective module

Pamela Suarez

$\tau$-tilting modules over one-point extensions by a projective module

Representation Theory 2017-05-23 v1

Authors: Pamela Suarez

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 $\tau$ -tilting $B$ -module is a support $\tau$ -tilting $A$ -module; and, conversely, the restriction of a given support $\tau$ -tilting $A$ -module is a support $\tau$ -tilting $B$ -module. Moreover, we prove that there exists a full embedding of quivers between the corresponding poset of support $\tau$ -tilting modules.

Keywords

gorenstein-projective modules module theory extension theorems

Cite

@article{arxiv.1705.07233,
  title  = {$\tau$-tilting modules over one-point extensions by a projective module},
  author = {Pamela Suarez},
  journal= {arXiv preprint arXiv:1705.07233},
  year   = {2017}
}

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