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

Abstract

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

arXiv comment11 Pages,Typos and errors have been corrected