Journal ArticleDOI
The φ-dimension of cyclic Nakayama algebras
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In this paper, the φ function for cyclic Nakayama algebras of infinite global dimension was studied, and the behavior of φ functions was shown to be invariant to the number of vertices.Abstract:
Igusa and Todorov introduced the φ function which generalizes the notion of projective dimension. We study the behavior of the φ function for cyclic Nakayama algebras of infinite global dimension. ...read more
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The finitistic dimension of a Nakayama algebra
TL;DR: In this article, it was shown that the finitistic dimension of A and its opposite algebra are equal for any Nakayama algebra A, and that the number of simple modules S with e (S ) = z is equal to the number S S ∈ N with e Ω(S ǫ) = z.
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τ-Cluster morphism categories and picture groups
Eric J. Hanson,Kiyoshi Igusa +1 more
TL;DR: In this article, the classifying space of τ-cluster morphism categories was shown to be the same as the space of cluster morphism classes defined by Igusa and Todorov.
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Nakayama Algebras which are Higher Auslander Algebras
TL;DR: In this article, it was shown that any cyclic Nakayama algebra which is higher Auslander algebra can be uniquely constructed from smaller ranks by reversing syzygy filtration process.
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Delooping level of Nakayama algebras
TL;DR: In this paper, the authors give another proof of the recent result of Ringel, which asserts equality between the finitistic dimension and delooping level of Nakayama algebras.
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Delooping Level of Nakayama algebras
TL;DR: In this article, the authors give another proof of the recent result of Ringel, which asserts equality between the finitistic dimension and delooping level of Nakayama algebras.
References
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Journal ArticleDOI
Representation dimension of exterior algebras
TL;DR: In this paper, it was shown that the Loewy length of a group algebra over F 2 of a finite group is strictly bounded below by the 2-rank of the group.
On the finitistic global dimension conjecture for artin algebras
Kiyoshi Igusa,Gordana Todorov +1 more
TL;DR: In this article, a simple condition which implies finiteness of the finitistic global dimension conjecture for artin algebras is given, which is a generalization of the radical cubed zero case since all syzygies have radical square zero in that case.
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The Gorenstein projective modules for the Nakayama algebras. I
TL;DR: In this paper, the authors outline the structure of the category of the Gorenstein projective Λ-modules, where Λ is a Nakayama algebra, and introduce the resolution quiver of Λ.
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Self-injective Right Artinian Rings and Igusa Todorov Functions
TL;DR: In this paper, it was shown that a right artin ring R is self-injective if and only if ψ(M) = 0 (or equivalently φ(M)) = 0 for all finitely generated right R-modules M, where ψ, φ :\!\! \mod R \to \mathbb N$