On $\tau$-tilting graphs for quasi-silted algebras

Wei Dai; Changjian Fu; Shengfei Geng; Pin Liu

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arXiv · 2401.05158

On $\tau$-tilting graphs for quasi-silted algebras

Wei Dai·Changjian Fu·Shengfei Geng·Pin Liu

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Abstract

We prove that the $\tau$-tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes $\tau$-reduction and wall and chamber structures. In particular, we observe a sufficient condition on the wall and chamber structure under which the connectivity of $\tau$-tilting graphs is preserved under taking quotients of algebras. As an immediate consequence, the connectivity of $\tau$-tilting graphs is also established for several new classes of algebras.

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BibTeX RIS

Wei Dai, Changjian Fu, Shengfei Geng, Pin Liu. 2024-01-10. On $\tau$-tilting graphs for quasi-silted algebras. https://arxiv.org/abs/2401.05158

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