2024/10/25 by Endre S. Rundsveen, Rundsveen, Endre S., Laertis Vaso +1
Mathematics · #16G20 #16S90 #18E10 #18G99 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2410.19505
openalex publication_date 2024/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Support τ-tilting pairs, functorially finite torsion classes and 2-term silting complexes are three much studied concepts in the representation theory of finite-dimensional algebras, which moreover turn out to be connected via work of Adachi, Iyama and Reiten. We investigate their higher-dimensional analogues via τd-rigid pairs, d-torsion classes and (d+1)-term silting complexes as well as the connections between these three concepts. Our work is done in the setting of truncated linear Nakayama algebras Λ(n,l)=k \mathbbAn/radk \mathbbAnl admitting a d-cluster tilting module. More specifically, we classify τd-rigid pairs (M,P) of Λ(n,l) with |M|+|P|=n via an explicit combinatorial description and show that they can be characterized by a certain maximality condition as well as by giving rise to a (d+1)-term silting complex in Kb(proj(Λ(n,l))). We also describe all d-torsion classes of Λ(n,l). Finally, we compare our results to the classical case d=1 and investigate mutation with a special emphasis on the case where d equals the global dimension of Λ.