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Fans and polytopes in tilting theory III: Classification of convex -fans of rank 3
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union of the simplices a…
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…
Tilting theory for hypersurface singularities of dimension one
Osamu Iyama, Junyang Liu
Any -graded commutative Gorenstein ring of Krull dimension one with a field admits a standard silting object in the stable category $\underline{\mathrm{CM…
Brick-splitting Torsion Pairs and Left Modularity
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-…
Schur roots and tilting modules of acyclic quivers over commutative rings
Osamu Iyama, Yuta Kimura
Let be a finite acyclic quiver and the cluster algebra of . It is well-known that for each field , the additive equivalence classes of support tilting -modules…
Total preprojective algebras
Aaron Chan, Osamu Iyama, Rene Marczinzik
We introduce total preprojective algebras of path algebras of Dynkin quivers , and prove that they are isomorphic to -Auslander algebras of preprojective algebras of…