Elements of the Representation Theory of Associative Algebras

By Daniel Simson, Andrzej Skowronski. 2007

1,745 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/db352d8824f395f3171e992fa2095a8b104d321c

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Citations in the corpus

Tilting-Connected Symmetric Algebras (2010, background): “ HomA(E,M) = 0 for any E ∈ E}. For any A-module X, we simply write ⊥X (respectively, X⊥) instead of ⊥(addX) (respectively, (addX)⊥). We recall the deﬁnition of a torsion class. Deﬁnition-Theorem 4.1. [ASS] Let C be a full subcategory of modA. We say that C is a torsion class in modA if C is closed u”
An introduction to higher Auslander–Reiten theory (2016, background): “n, ϕ factors through the epimorphism HomΛ(L,τdX) → δ∗(τdX) due to the projectivity of HomΛ(LX,L). Finally, by Yoneda’s lemma, the required morphism is induced by some h: L → LX (see also Lemma VI.3.1 [ASS06]). AN INTRODUCTION TO HIGHER AUSLANDER–REITEN THEORY 21 By the dual of 2.19 and 2.12 there ex”
Periodicities of T-systems and Y-systems (2008, methodology): “The following description of indecomposable objects in CQ follows from Gabriel’s Theorem [ASS] and Fomin-Zelevinsky’s description of finite type cluster algebras [FZ2].”
Wall and chamber structure for finite-dimensional algebras (2018, background): “lgebra of the one-punctured torus, and have been object of intense studies in the context of cluster algebras, see for instance [30, Example 35], [32] or [15, Theorem 5.17]. We refer to the textbooks [5, 3, 35] for background material. 1.2 Acknowledgements This paper is a revised version of one part”
Quiver varieties and cluster algebras (2009, neutral): “Tilting modules.”
The periodicity conjecture for pairs of Dynkin diagrams (2010, methodology): “[2], [3], [29], [63]) between the category of modules over the path algebra kQ and the category of representations of the opposite quiver Qop: It sends a module M over the path algebra to the representation V of Qop whose value at the vertex i is Vi = Mei and which maps an arrow α : i → j to the lin”
Degenerate flag varieties of type A and C are Schubert varieties (2014, positive): “ → αi+1,j (for every 1 ≤ i < j ≤ n) and an oriented edge αi,j → αi,j+1 (for 1 ≤ i ≤ j<n). The quiver Γn is the famous Auslander-Reiten quiver of the equioriented type A quiver algebra (see e.g. [1]). For future reference we embed the quiver Γn into the decorated quiver Γ˜n obtained from Γn by ”