Author

Da-Jun Liu

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Preprint Sep 2026

Relative Derived Delooping Levels and $\tau$-Tilting Modules

Let $\mathcal{E}$ be an essentially small idempotent-complete exact category with enough projective objects. We develop derived delooping levels in $\mathcal{E}$. We apply this framework to a basic support $\tau$-tilting module $T$. We then define the derived delooping level relative to $T$ and compare it with the ordi...

Han-Peng Gao, Da-Jun Liu, Hou-Jun Zhang · 2 citations · ⚡1

Preprint Sep 2026

Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions

Let $B$ be a finite-dimensional algebra, $M\in\modu B$, and $A=B[M]$ the one-point extension. We give a stable two-step extension criterion for the new simple $A$-module to have derived delooping level at most one. For a concrete algebra $B$ with a self-injective Nakayama quotient $R$, we determine the derived and clas...

Han-Peng Gao, Da-Jun Liu, Ruo-Mu Xu · 2 citations · ⚡1