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arxiv: 2501.02466 · v1 · pith:4QXNX7BOnew · submitted 2025-01-05 · 🧮 math.RT · math.RA

Comparing τ-tilting modules and 1-tilting modules

classification 🧮 math.RT math.RA
keywords tiltingmodulescharacterizeconditionconjecturedeloopingmodulesatisfying
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. $\tau$-tilting modules, depth and delooping level

    math.RT 2026-06 unverdicted novelty 7.0

    Depth and delooping level relative to Fac T bound finitistic dimension of B^op, implying it is finite when A is minimal representation-infinite or of finite representation type.

  2. $\tau$-tilting modules, depth and delooping level

    math.RT 2026-06 unverdicted novelty 6.0

    Introduces depth and delooping level relative to τ-tilting modules and proves that finitistic dimension of End_A(T)^op is bounded by these invariants, implying finiteness in two classes of algebras.