1 citations · 1 across the 13 of their papers we have counts for
14 papers
Preprojective algebras and generalisations: A short survey
Aaron Chan, Osamu Iyama, Rene Marczinzik
The preprojective algebra of a hereditary algebra can be defined as a certain orbit construction of the regular representation generated by the Auslander-Reiten translation. In…
Left modularity and extremality for (some) infinite lattices
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for…
Fractionally Calabi-Yau algebras and cluster tilting
Aaron Chan, Osamu Iyama, Rene Marczinzik
We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of -cluster tilting modules over $d…
Triangle equivalences between Gorenstein tiled orders and incidence algebras of posets
Osamu Iyama, Junyang Liu
We prove that for any -graded Gorenstein tiled order , the stable category is triangle equivalent to the perfect derived cate…
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…
On -tilting theory
Takahide Adachi, Osamu Iyama, Idun Reiten
We give a brief introduction to -tilting theory [AIR]. In particular, we will see how our theory unifies two different branches of tilting theory, namely, silting theory and clu…
Auslander-Reiten's Cohen-Macaulay algebras and contracted preprojective algebras
Aaron Chan, Osamu Iyama, Rene Marczinzik
Auslander and Reiten called a finite dimensional algebra over a field Cohen-Macaulay if there is an -bimodule which gives an equivalence between the category of finitely…
Torsion classes of extended Dynkin quivers over commutative rings
Osamu Iyama, Yuta Kimura
For a Noetherian -algebra , there is a canonical inclusion , and each element in the…
Dominant Auslander-Gorenstein algebras and mixed cluster tilting
Aaron Chan, Osamu Iyama, Rene Marczinzik
We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic pr…