Lifting to cluster-tilting objects in 2-Calabi-Yau triangulated categories
Changjian Fu, Pin Liu
TL;DR
This paper proves that tilting modules over endomorphism algebras of cluster-tilting objects in 2-Calabi-Yau categories can be lifted to cluster-tilting objects, extending previous results in cluster categories.
Contribution
It generalizes the lifting property of tilting modules to a broader class of 2-Calabi-Yau triangulated categories.
Findings
Tilting modules lift to cluster-tilting objects in 2-Calabi-Yau categories.
Generalizes previous results from cluster categories.
Provides a new understanding of the structure of 2-Calabi-Yau categories.
Abstract
We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi-Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi-Yau triangulated category. This generalizes a recent work of D. Smith for cluster categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons