9 papers · 1 filter
Calabi-Yau structures on derived and singularity categories of symmetric orders
Norihiro Hanihara, Junyang Liu
We construct left and right Calabi-Yau structures on derived respectively singularity categories of symmetric orders over commutative Gorenstein rings . For this, we first c…
Silting correspondences and Calabi-Yau dg algebras
Norihiro Hanihara, Osamu Iyama
This paper is devoted to studying two important classes of objects in triangulated categories; silting objects and -cluster tilting objects, and their correspondences. First, we…
Reflexive modules and Auslander-type conditions
Norihiro Hanihara
We study the category of reflexive modules over a two-sided Noetherian ring . We show that the category is quasi-abelian if and…
Calabi-Yau completions for roots of dualizing dg bimodules
Norihiro Hanihara
Roots of shifted Serre functors appear naturally in representation theory and algebraic geometry. We give an analogue of Keller's Calabi-Yau completion for roots of shifted inverse…
Higher hereditary algebras and Calabi-Yau algebras arising from some toric singularities
Norihiro Hanihara
We study graded and ungraded singularity categories of some commutative Gorenstein toric singularities, namely, Veronese subrings of polynomial rings, and Segre products of some co…
Morita theorem for hereditary Calabi-Yau categories
Norihiro Hanihara
We give a structure theorem for Calabi-Yau triangulated category with a hereditary cluster tilting object. We prove that an algebraic -Calabi-Yau triangulated category with a $d…