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Jennifer A. Firkins Nordstrom 《代数通讯》2013,41(2):567-583
In this article, we generalize the definition of a Gabriel quiver in order to provide an analogous combinatorial object for the study of certain locally Artinian rings. We are then able to extend Gabriel's Theorem to locally unipotent rings whose generalized left and right quivers are trees. 相似文献
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InnerAsociativeRingsW.B.VasanthaKandasamy(Dept.ofMath.,IndianInstituteofTechnologyMadras-600036,India)AbstractInfluencedbyth... 相似文献
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设Ω是有限结合环类中全部弱单环组成的环类,Ω1∪Ω2=Ω,Ω1∩Ω2=Φ,在有限结合环类中,我们证明了LΩ1=UΩ2可以成立,并给出等式成立的充要条件.使用这个结论,我们可以证明,在有限结合环类中,超幂零根是特殊根. 相似文献
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Nikolay Silkin 《代数通讯》2013,41(9):3187-3205
If all finitely generated rings in a variety of associative rings satisfy the ascending chain condition on two-sided ideals, the variety is called locally weak noetherian. If there is an upper bound on nilpotency indices of nilpotent rings in a variety, the variety is called a finite index variety. We prove that the join of a finitely based locally weak noetherian variety and a variety of finite index is also finitely based and locally weak noetherian. One consequence of this result is that if an associative ring variety is connected by a finite path in the lattice of all associative ring varieties to a finitely based locally weak noetherian variety then such variety is also finitely based and locally weak noetherian. 相似文献
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We investigate representations of *-algebras associated with posets. Unitarizable representations of the corresponding (bound) quivers (which are polystable representations for some appropriately chosen slope function) give rise to representations of these algebras. Considering posets which correspond to unbound quivers this leads to an ADE-classification which describes the unitarization behaviour of their representations. Considering posets which correspond to bound quivers, it is possible to construct unitarizable representations starting with polystable representations of related unbound quivers which can be glued together with a suitable direct sum of simple representations. Finally, we estimate the number of complex parameters parametrizing irreducible unitary non-equivalent representations of the corresponding algebras. 相似文献
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ABSTRACT We study self-dual coradically graded pointed Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras (van Oystaeyen and Zhang, 2004). The co-Gabriel Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional pointed Hopf algebras with self-dual graded versions are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider (2000) and may help to classify finite dimensional self-dual coradically graded pointed Hopf algebras. 相似文献
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S. I. Tsupiy 《Journal of Mathematical Sciences》2007,144(2):4023-4029
In this paper, the set of quivers of semi-maximal rings is investigated. It is proved that the elements of this set are formed
by the elements of the set of quivers of tiled orders and that the set of quivers of tiled orders with n vertices is determined by the integer points of a convex polyhedral domain that lie in the nonnegative part of the space
. It is also proved that the set of quivers of tiled orders with n vertices contains all simple, oriented, strongly connected graphs with n vertices and n loops, does not contain any graphs with n vertices and n − 1 loops, and contains only a part of the graphs with n vertices and m (m < n − 1) loops.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 215–223, 2005. 相似文献
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Uriya A. First 《代数通讯》2013,41(6):2567-2582
We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors. 相似文献
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Roger Bielawski 《manuscripta mathematica》2013,141(1-2):29-49
We produce natural quadratic Poisson structures on moduli spaces of representations of quivers. In particular, we study a natural Poisson structure for the generalised Kronecker quiver with 3 arrows. 相似文献
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《代数通讯》2013,41(10):3467-3478
In the first part of this article, we describe the projective representations in the category of representations by modules of a quiver which does not contain any cycles and the quiver A ∞ as a subquiver, that is, the so-called rooted quivers. As a consequence of this, we show when the category of representations by modules of a quiver admits projective covers. In the second part, we develop a technique involving matrix computations for the quiver A ∞, which will allow us to characterize the projective representations of A ∞. This will improve some previous results and make more accurate the statement made in Benson (1991). We think this technique can be applied in many other general situations to provide information about the decomposition of a projective module. 相似文献
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We present necessary and sufficient conditions for the finite representability of K-marked quivers. 相似文献
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《代数通讯》2013,41(4):1777-1797
Abstract In this paper we introduce and study the local quiver as a tool to investigate the étale local structure of moduli spaces of θ-semistable representations of quivers. As an application we determine the dimension vectors associated to irreducible representations of the torus knot groups G p,q = ?a, b ∣ a p = b q ?. 相似文献
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Let H be a Hopf algebra with a finite-dimensional, nontrivial space of skew primitive elements, over an algebraically closed field of characteristic zero. We prove that H contains either the polynomial algebra as a Hopf subalgebra, or a certain Schurian simple-pointed Hopf subalgebra. As a consequence, a complete list of the locally finite, simple-pointed Hopf algebras is obtained. Also, the graded automorphism group of a Hopf algebra on a Schurian Hopf quiver is determined, and the relation between this group and the automorphism groups of the corresponding Hopf quiver, is clarified. 相似文献
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Yu-Han Liu 《Algebras and Representation Theory》2014,17(2):593-621
We study natural Grothendieck topologies on categories of quivers without and with relations, prove descent theorems for quiver representations, and introduce the notion of torsors over quivers. 相似文献