Exchange graphs and Ext quivers
نویسندگان
چکیده
منابع مشابه
Bipartite Graphs, Quivers, and Cluster Variables
We explore connections between formulas for certain combinatorial and algebraic objects. In particular, given a planar bipartite graph G, we consider the cluster algebra A corresponding to a quiver obtained from its dual graph. We then obtain formulas for certain cluster variables in A in terms of perfect matchings of subgraphs of G. Such subgraphs look like trees; locally they look like snakes...
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If A and B are Abelian groups, then Hom(A,B) is also an Abelian group under pointwise addition of functions. In this section we will see how Hom gives rise to classes of functors. Let A denote the category of Abelian groups. A covariant functor T : A → A associates to every Abelian group A an Abelian group T (A), and for every homomorphism f : A → B a homomorphism T (f) : T (A)→ T (B), such tha...
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We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of symmetric quivers, in particular we describe the indecom-posable symmetric representations. Their dimensions constitute root systems corresponding to certain symme...
متن کاملQuivers, Quotients, and Duality
We give a direct computational proof of N = 2 Seiberg duality for arbitrary quivers, and find the action on the Fayet-Iliopoulos parameters. We also find a new analogous classical duality for Kähler potentials of N = 1 quivers that generalizes the trivial duality Gr(N,N+M) ≃ Gr(M,N+M) for Grassmannians. [email protected] Roč[email protected]
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1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.08.017