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Ralf Schiffler - One of the best experts on this subject based on the ideXlab platform.
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on the first hochschild Cohomology Group of a cluster tilted algebra
Algebras and Representation Theory, 2015Co-Authors: Ibrahim Assem, Maria Julia Redondo, Ralf SchifflerAbstract:Given a cluster-tilted algebra B, we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a k-vector space, to the direct sum of \({\text {HH}}^{1}(C)\) with \(k^{n_{B,C}}\), where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.
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the first hochschild Cohomology Group of a cluster tilted algebra revisited
International Journal of Algebra and Computation, 2013Co-Authors: Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa, Ralf SchifflerAbstract:Given a cluster-tilted algebra B we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by , then we prove that HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with HH1(B,E). This yields homological interpretations for results of the first and the fourth authors with M. J. Redondo.
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the first hochschild Cohomology Group of a cluster tilted algebra revisited
arXiv: Representation Theory, 2012Co-Authors: Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa, Ralf SchifflerAbstract:Given a cluster-tilted algebra B we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by E= Ext2(DC,C), then we prove that HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with HH1(B,E). This yields homological interpretations for results of the first and the fourth author with M.J. Redondo.
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On the first Hochschild Cohomology Group of a cluster-tilted algebra
2012Co-Authors: Ibrahim Assem, Maria Redondo, Ralf SchifflerAbstract:Given a cluster-tilted algebra B, we study its first Hochschild Cohomology Group HH^1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation extension of C, then we show that if C is constrained, or else if B is tame, then HH^1(B) is isomorphic, as a k-vector space, to the direct sum of HH^1(C) with k^{n_{B,C}}, where n_{B,C} is an invariant linking the bound quivers of B and C. In the representation-finite case, HH^1(B) can be read off simply by looking at the quiver of B.
Ibrahim Assem - One of the best experts on this subject based on the ideXlab platform.
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on the first hochschild Cohomology Group of a cluster tilted algebra
Algebras and Representation Theory, 2015Co-Authors: Ibrahim Assem, Maria Julia Redondo, Ralf SchifflerAbstract:Given a cluster-tilted algebra B, we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a k-vector space, to the direct sum of \({\text {HH}}^{1}(C)\) with \(k^{n_{B,C}}\), where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.
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the first hochschild Cohomology Group of a cluster tilted algebra revisited
International Journal of Algebra and Computation, 2013Co-Authors: Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa, Ralf SchifflerAbstract:Given a cluster-tilted algebra B we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by , then we prove that HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with HH1(B,E). This yields homological interpretations for results of the first and the fourth authors with M. J. Redondo.
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the first hochschild Cohomology Group of a cluster tilted algebra revisited
arXiv: Representation Theory, 2012Co-Authors: Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa, Ralf SchifflerAbstract:Given a cluster-tilted algebra B we study its first Hochschild Cohomology Group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by E= Ext2(DC,C), then we prove that HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with HH1(B,E). This yields homological interpretations for results of the first and the fourth author with M.J. Redondo.
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On the first Hochschild Cohomology Group of a cluster-tilted algebra
2012Co-Authors: Ibrahim Assem, Maria Redondo, Ralf SchifflerAbstract:Given a cluster-tilted algebra B, we study its first Hochschild Cohomology Group HH^1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation extension of C, then we show that if C is constrained, or else if B is tame, then HH^1(B) is isomorphic, as a k-vector space, to the direct sum of HH^1(C) with k^{n_{B,C}}, where n_{B,C} is an invariant linking the bound quivers of B and C. In the representation-finite case, HH^1(B) can be read off simply by looking at the quiver of B.
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the first hochschild Cohomology Group of a schurian cluster tilted algebra
Manuscripta Mathematica, 2009Co-Authors: Ibrahim Assem, Maria Julia RedondoAbstract:AbstractGiven a cluster-tilted algebra B we study its first Hochschild coho-mology Group HH 1 (B) with coefficients in the B-B-bimodule B. We findseveral consequences when B is representation-finite, and also in the casewhere B is cluster-tilted of type A˜.2000 Mathematics Subject Classification : 16E40 1 Introduction Cluster categories were introduced in [11] and also in [17] for type A, in order tounderstand better the cluster algebras of Fomin and Zelevinsky [20]. Cluster-tiltedalgebras were defined in [12] and also in [18] for type A. These algebras have beenstudied by several authors (see, for instance, [1, 18, 12, 13]). Our objective here is,for a cluster-tilted algebra B, to study its first Hochschild Cohomology Group HH 1 (B)with coefficients in the B-B-bimodule B, see [19]. As a first step, we consider thecase where B is schurian: this includes the case of all representation-finite cluster-tiltedalgebras. There are several reasons for this restriction. Indeed, it was shown in [1]that, if C is a tilted algebra, then the trivial extension C ⋉ Ext
Ueda Kazushi - One of the best experts on this subject based on the ideXlab platform.
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Homological mirror symmetry for Milnor fibers of simple singularities
2021Co-Authors: Lekili Yanki, Ueda KazushiAbstract:We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the Hochschild Cohomology Group of the derived $n$-preprojective algebra of a Dynkin quiver for any $n \geq 1$, and the symplectic Cohomology Group of the Milnor fiber of any simple singularity in any dimension greater than one.Comment: 23 pages, revised following the suggestions of the referee
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Homological mirror symmetry for Milnor fibers of simple singularities
2020Co-Authors: Lekili Yanki, Ueda KazushiAbstract:We prove homological mirror symmetry for Milnor fibers of simple singularities, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the symplectic Cohomology Group of the Milnor fiber of a simple singularity in all dimensions.Comment: 20 page
Alexey Ananyevskiy - One of the best experts on this subject based on the ideXlab platform.
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on the zeroth stable a1 homotopy Group of a smooth curve
Journal of Pure and Applied Algebra, 2017Co-Authors: Alexey AnanyevskiyAbstract:Abstract We provide a cohomological interpretation of the zeroth stable A 1 -homotopy Group of a smooth curve over an infinite perfect field. We show that this Group is isomorphic to the first Nisnevich (or Zariski) Cohomology Group of a certain sheaf closely related to the first Milnor–Witt K-theory sheaf. This Cohomology Group can be computed using an explicit Gersten-type complex. We show that if the base field is algebraically closed then the zeroth stable A 1 -homotopy Group of a smooth curve coincides with the zeroth Suslin homology Group that was identified by Suslin and Voevodsky with a relative Picard Group. As a consequence we reobtain a version of Suslin's rigidity theorem.
Monica Musso - One of the best experts on this subject based on the ideXlab platform.
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singular limits for the bi laplacian operator with exponential nonlinearity in r4
Annales De L Institut Henri Poincare-analyse Non Lineaire, 2008Co-Authors: Monica Clapp, Claudio Munoz, Monica MussoAbstract:Abstract Let Ω be a bounded smooth domain in R 4 such that for some integer d ⩾ 1 its d-th singular Cohomology Group with coefficients in some field is not zero, then problem { Δ 2 u − ρ 4 k ( x ) e u = 0 in Ω , u = Δ u = 0 on ∂ Ω , has a solution blowing-up, as ρ → 0 , at m points of Ω, for any given number m.
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singular limits for the bi laplacian operator with exponential nonlinearity in r 4
arXiv: Analysis of PDEs, 2007Co-Authors: Monica Clapp, Claudio Munoz, Monica MussoAbstract:Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for some integer $d\geq1$ its $d$-th singular Cohomology Group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any given number $m$.