2016
DOI: 10.1007/s10468-016-9608-5
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On n-cubic Pyramid Algebras

Abstract: In this paper we study a class of algebras having n-dimensional pyramid shaped quiver with n-cubic cells, which we called n-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic n-Auslander absolutely n-complete algebras introduced by Iyama. We show that the projective resolutions of the simples of n-cubic pyramid algebras can be characterized by n-cuboids, and prove that they are periodic. So these algebras are almost Koszul and (n − 1)-translation algebras. We also recover I… Show more

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Cited by 12 publications
(13 citation statements)
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“…Using results in this paper, we point out that the Auslander Reiten quiver of the cone M of Iyama's absolute n-complete algebra T 4 n (k) can also be obtained as a truncation from the quiver of the 0-extension of an n-translation algebra for n = 1, 2, · · · (For the detail and for general case see [18]).…”
Section: Examplesmentioning
confidence: 93%
See 2 more Smart Citations
“…Using results in this paper, we point out that the Auslander Reiten quiver of the cone M of Iyama's absolute n-complete algebra T 4 n (k) can also be obtained as a truncation from the quiver of the 0-extension of an n-translation algebra for n = 1, 2, · · · (For the detail and for general case see [18]).…”
Section: Examplesmentioning
confidence: 93%
“…The following examples show how n-translation algebra are applied to the path algebra of Dynkin type. In [18], we present some classes of n-translation algebras related to higher representation theory [23,20].…”
Section: Examplesmentioning
confidence: 99%
See 1 more Smart Citation
“…The above idea for the finite type is used in [12] to study the iterated construction of the n-cubic algebras, whose quadratic dual are n-representation-finite algebras of type A (absolutely n-complete algebras in [20]). In fact, [12] can be regarded as an example of τ n -finite case of our main result in this section, which tell us how to find τ -mature subquiver of Z| n−1 Q for certain (n − 1)-representation-finite algebra kQ/(ρ) of the type A with bound quiver Q = (Q 0 , Q 1 , ρ). Now assume that Γ is an acyclic (n − 1)-mesh algebra with bound quiver Q ⊥ = (Q 0 , Q 1 , ρ ⊥ ) and let Λ be its quadratic dual with bound quiver Q = (Q 0 , Q 1 , ρ).…”
Section: Example Preprojective and Preinjective Components Of Heredit...mentioning
confidence: 99%
“…we have eY t ≃ X t . By applying Hom Γ (Γe, ) on (10), we get an exact sequence of Γ-modules from (12),…”
mentioning
confidence: 99%