Strongly Gorenstein-projective Quiver 
		Representations

Teng-xia, JU; Luo, Xiu-Hua

doi:10.11650/tjm/201103

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…It turns out that the category of the (strongly) Gorenstein-projective modules is closely related to the submodule category [18,36]. Motivated by the relation between submodule categories and the construction of Gorenstein-projective modules over triangular matrix rings, more general methods of constructing Gorenstein-projective modules over tensor algebras have been recently developed [13,15,19,20,37], using monomorphism categories. For instance, we will use the following result: Theorem 4.1] Let Q be an acyclic quiver, I an monomial ideal of kQ and A a finite dimensional algebra over a field k.…”

Section: Introductionmentioning

confidence: 99%

Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules

Luo¹,

Zhu²

2022

Preprint

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Given a finite dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ = A ⊗ k kQ/I, where kQ is the path algebra of Q over k and I is a monomial ideal. We show that (X , Y) is a (complete) hereditary cotorsion pair in A-mod if and only if (smon(Q, I, X ), rep(Q, I, Y)) is a (complete) hereditary cotorsion pair in Λ-mod. We also show that A is left weakly Gorenstein if and only if so is Λ. Provided that kQ/I is non-semisimple, the category ⊥ Λ of semi-Gorenstein-projective Λ-modules coincides with the category of separated monic representations smon(Q, I, ⊥ A) if and only if A is left weakly Gorenstein.

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Section: Introductionmentioning

confidence: 99%

Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules

Luo¹,

Zhu²

2022

Preprint

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“…These strongly Gorenstein-projective modules are being well-studied by many authors under different contexts (see e.g. [17] and its references).…”

Section: Introductionmentioning

confidence: 99%

A note on deformations of Gorenstein-projective modules over finite dimensional algebras

Vélez-Marulanda

2019

rev.colomb.mat

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Let k be a fixed field of arbitrary characteristic, and let Λ be a finite dimensional k-algebra. Assume that V is a left Λ-module of finite dimension over k. F. M. Bleher and the author previously proved that V has a well-defined versal deformation ring R(Λ, V ) which is a local complete commutative Noetherian ring with residue field isomorphic to k. Moreover, R(Λ, V ) is universal if the endomorphism ring of V is isomorphic to k. In this article we prove that if Λ is a basic connected Nakayama algebra without simple modules and V is a Gorenstein-projective left Λ-module, then R(Λ, V ) is universal. Moreover, we also prove that the universal deformation rings R(Λ, V ) and R(Λ, ΩV ) are isomorphic, where ΩV denotes the first syzygy of V . This result extends the one obtained by F. M. Bleher and D. J. Wackwitz concerning universal deformation rings of finitely generated modules over self-injective Nakayama algebras. In addition, we also prove the following result concerning versal deformation rings of finitely generated modules over triangular matrix finite dimensional algebras. Let Σ = Λ B 0 Γ be a triangular matrix finite dimensional Gorenstein k-algebra with Γ of finite global dimension and B projective as a left Λ-module. If V W f is a finitely generated Gorenstein-projective left Σ-module, then the versal deformation rings R Σ, V W f and R(Λ, V ) are isomorphic.2010 Mathematics Subject Classification. 16G10 and 16G20 and 20C20. Key words and phrases. (Uni)versal deformation rings and finitely generated Gorenstein-projective modules and Nakayama algebras and triangular matrix algebras.

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A short note on deformations of (strongly) Gorenstein-projective modules over the dual numbers

Vélez-Marulanda,

Suárez

2024

São Paulo J. Math. Sci.

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Strongly Gorenstein-projective Quiver Representations

Cited by 4 publications

References 25 publications

Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules

Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules

A note on deformations of Gorenstein-projective modules over finite dimensional algebras

A short note on deformations of (strongly) Gorenstein-projective modules over the dual numbers

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