Classification of silted algebras for two quivers of Dynkin type \mathbbA_n

2025/04/21 by Xie, Zongzhen, Yang, Dong, Zhang, Houjun
#2-term silting complex #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #rooted quiver with relation #shod algebra #silted algebra #tilted algebra

paper · doi:10.48550/arxiv.2504.14789

Abstract

In this paper, we give a complete classification of silted algebras for the quiver \overrightarrow\mathbbA_n of type \mathbbA_n with linear orientation and for the quiver obtained from \overrightarrow\mathbbA_n by reversing the arrow at the unique source. Based on the classification, we also compute the number of silted algebras for these two quivers.

Citations

• There are no strictly shod algebras in hereditary gentle algebras
• Some examples of silted algebras of Dynkin type
• Some examples of t-structures for finite-dimensional algebras
• Derived equivalences via HRS-tilting
• Infinity-tilting theory
• Endomorphism algebras of 2-term silting complexes
• Realisation functors in tilting theory
• Silted algebras
• A silting theorem
• Silting reduction and Calabi--Yau reduction of triangulated categories
• The numbers of support-tilting modules for a Dynkin algebra
• Silting mutation in triangulated categories
• Noncrossing partitions and representations of quivers
• COXETER FUNCTORS AND GABRIEL'S THEOREM

Related

• Classification of silted algebras for two quivers of Dynkin type \mathbbD_n
• Classification silted algebras for a quiver of Dynkin type \mathbbA_n via geometric models
• Some examples of silted algebras of Dynkin type
• The Representation Theory of Dynkin Quivers. Three Contributions
• On the quiver with relations of a quasitilted algebra and applications