Silting and tilting objects in cleft extensions of abelian categories
Abstract
We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then we apply our results to the cleft extensions of module categories, and characterize silting and tilting modules over $θ$-extension of rings. Some known results over trivial extension of rings are extended and strengthened.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Rings
Modules
and Algebras
Advanced Topics in Algebra
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint