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In this paper we discuss, in terms of quiver with relations, su?cient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension at most two and we give a su?cient condition to be a quasitilted algebra. We show that this condition is not necessary. In the case of a strongly simply connected schurian algebra, we discuss necessary conditions, and combining both types of conditions, we are able to analyze if some given algebra is quasitilted. As an application we obtain the quiver with relations of all the tilted and cluster tilted algebras of Dynkin type Ep. 相似文献
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A. A. Yakovleva 《Journal of Mathematical Sciences》1998,89(2):1172-1179
Representations of a quiver that is a chain of commutative squares are studied. It is proved that the problem of classification
of representations of such a quiver is a tame problem, and a structure of representations is given. This result is a generalization
of several known results concerning some important matrix problems. Bibliography:3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 140–151. 相似文献
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Christine Bessenrodt 《Mathematische Zeitschrift》1991,206(1):25-34
This work has been supported by the DFG project “Darstellungstheorie” at the University of Essen. 相似文献
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We construct bar-invariant Z[q ±1/2 ]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases. 相似文献
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We obtain explicit generators for the centre of the Ringel-Hall algebra of a cyclic quiver and define a canonical algebra
monomorphism from Macdonald's ring of symmetric functions to the centre, which furthermore respects the comultiplication and
the symmetric bilinear form.
Dedicated to Claus Michael Ringel on the occasion of his 60th birthday 相似文献
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Götz Pfeiffer 《Advances in Mathematics》2009,220(5):1428-1465
The descent algebra Σ(W) is a subalgebra of the group algebra QW of a finite Coxeter group W, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of W. Thus Σ(W) is a basic algebra, and as such it has a presentation as a quiver with relations. Here we construct Σ(W) as a quotient of a subalgebra of the path algebra of the Hasse diagram of the Boolean lattice of all subsets of S, the set of simple reflections in W. From this construction we obtain some general information about the quiver of Σ(W) and an algorithm for the construction of a quiver presentation for the descent algebra Σ(W) of any given finite Coxeter group W. 相似文献
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On the Hochschild (co)homology of a monomial algebra given by a cyclic quiver and two zero-relations
Tomohiro Itagaki 《代数通讯》2017,45(5):2052-2073
Let K be an algebraically closed field and Γ a cyclic quiver. Xu and Wang investigated the Hochschild (co)homology groups of KΓ∕I, where I is an ideal of KΓ generated by one path. In this paper, in the case that I is an ideal of KΓ generated by two paths, we give the module structure of the Hochschild (co)homology groups of KΓ∕I. 相似文献
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Michael Falk 《Advances in Mathematics》1990,80(2)
Let L be a geometric lattice. Following P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. math. 56 (1980), 167–189, we associate with L a graded commutative algebra A(L). In this paper we introduce a new invariant ψ of the algebra A(L) which suffices to distinguish algebras for which all other known invariants coincide. This result is applied to the study of arrangements of complex hyperplanes, with L being the intersection lattice. In this case A(L) is isomorphic to the cohomology algebra of the associated hyperplane complement. The goal is to find examples of arrangements with non-isomorphic lattices but homotopy equivalent complements. The invariant introduced here effectively narrows the list of candidates. Nevertheless, we exhibit combinatorially inequivalent arrangements for which all known invariants, including ψ, coincide. 相似文献
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We show that the Cuntz algebra can be represented as a crossed product of the canonical anticommutation relations algebra by an endomorphism. 相似文献
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Csaba Sz��nt�� 《Mathematische Zeitschrift》2011,269(3-4):833-846
We deduce using the Ringel?CHall algebra approach explicit formulas for the cardinalities of some Grassmannians over a finite field associated to the Kronecker quiver. We realize in this way a quantification of the formulas obtained by Caldero and Zelevinsky for the Euler characteristics of these Grassmannians. Finally we present a recursive algorithm for computing the cardinality of every Kronecker quiver Grassmannian over a finite field. 相似文献
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A. Letizia 《Acta Mathematica Hungarica》1980,36(1-2):63-64
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Acta Mathematica Hungarica - 相似文献
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Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial cardinality and we give different approaches to Euler characteristics. Our main result is the positivity of Euler characteristics when M is an exceptional module. This solves a conjecture of Fomin and Zelevinsky for acyclic cluster algebras. 相似文献
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