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