Comparing $\ddot{I}„$-tilting modules and $1$-tilting modules

Abstract

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

10 Pages. Any comments are welcome