Finiteness and Silting-Discreteness in Graded Gentle and Skew-Gentle Algebras
Analysis
This paper contributes to the understanding of representation theory of algebras, specifically focusing on gentle and skew-gentle algebras. It extends existing results on τ-tilting finiteness and characterizes silting-discreteness using geometric models (surfaces and orbifolds). The results are significant for researchers in algebra and related fields, providing new insights into the structure and properties of these algebras.
Key Takeaways
- •Extends the result for gentle algebras on τ-tilting finiteness to skew-gentle algebras.
- •Provides a geometric characterization of silting-discreteness for graded gentle and skew-gentle algebras using surface and orbifold models.
- •The findings offer insights into the representation theory of these specific types of algebras.
Reference
“A skew-gentle algebra is τ-tilting finite if and only if it is representation-finite.”