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arXiv · 2501.02466

Comparing $\tau$-tilting modules and $1$-tilting modules

Xiao-Wu Chen·Zhi-Wei Li·Xiaojin Zhang·Zhibing Zhao
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Abstract

We characterize $\tau$-tilting modules as $1$-tilting modules over quotient algebras satisfying a tensor-vanishing condition, and characterize $1$-tilting modules as $\tau$-tilting modules satisfying a ${\rm Tor}^1$-vanishing condition. We use delooping levels to study \emph{Self-orthogonal $\tau$-tilting Conjecture}: any self-orthogonal $\tau$-tilting module is $1$-tilting. We confirm the conjecture when the endomorphism algebra of the module has finite global delooping level.

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Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang, Zhibing Zhao. 2025-01-05. Comparing $\tau$-tilting modules and $1$-tilting modules. https://arxiv.org/abs/2501.02466

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