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math.RT2026
Auslander correspondence for higher stable dg categories and cluster Morita theory
Ryu Tomonaga
The notion of -stable dg categories axiomatizes -cluster tilting subcategories of stable dg categories. We establish an Auslander correspondence for -stable dg categories:…
math.RT2025
Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
Ryu Tomonaga
We prove the existence and give a classification of toric non-commutative crepant resolutions (NCCRs) of Gorenstein toric singularities whose divisor class group has rank one. More…
math.RT2025
On silting mutations preserving global dimension
Ryu Tomonaga
A -silting object is a silting object whose derived endomorphism algebra has global dimension or less. We give an equivalent condition, which can be stated in terms of dg qu…