AI 中文总结
本文为支撑τ-倾斜模构造相对悬浮，推广了Gélinas的结果，证明相对去环与普通去环指标相差一，并应用于循环Nakayama代数，得到其有限维数与去环水平相等。
AI 中文摘要
我们为支撑 $\tau$-倾斜模生成的精确范畴构造了相对悬浮，并通过所得伴随的单位刻画了高阶去环，这是Gélinas在Adv. Math.(2022)中结果的推广。我们证明了与普通高阶去环的比较需要在指标上平移一。更精确地，对于每个 $k,d\ge1$，存在一个模，其普通 $k$-去环水平为零，而相对水平为 $d$。我们还证明了张量归纳保持相对构造和诱导模上的高阶去环水平。作为应用，我们研究了具有任意局部系数和自同构扭曲的循环Nakayama代数。它们的左右小和大有限维数以及普通和导出去环水平都等于底层Nakayama代数的有限维数。
英文摘要
We construct relative suspension for the exact category generated by a support $τ$-tilting module and characterize higher delooping by the units of the resulting adjunction, which are the generalizations of Gélinas's results in Adv. Math.(2022). We prove that comparison with ordinary higher delooping requires a shift of one in the index. More precisely, for every $k,d\ge1$, there is a module whose ordinary $k$-delooping level is zero and whose relative level is $d$. We also prove that tensor induction preserves the relative constructions and higher delooping levels on induced modules. As an application, we study cyclic Nakayama algebras with arbitrary local coefficients and automorphism twists. Their left and right little and big finitistic dimensions and ordinary and derived delooping levels all equal the finitistic dimension of the underlying Nakayama algebra.
Comments22 pages
