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1.
雍锡琪 《数学研究》1996,29(2):86-87
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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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   

4.
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. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 215–223, 2005.  相似文献   

5.
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   

6.
《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 Benson , D. J. ( 1991 ). Representations and Cohomology I . Cambridge Studies in Advanced Mathematics , Vol. 30 . Cambridge : Cambridge University Press . [Google Scholar]). 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   

7.
We present necessary and sufficient conditions for the finite representability of K-marked quivers.  相似文献   

8.
《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 Q be a finite quiver without oriented cycles. Denote by U (Q) the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext (Q) l (U, U) = 0 for all l > 0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for when this algebra is isomorphic to the path algebra of the quiver Q. If so, then the bounded derived categories of finitely generated right k Q-modules and that of coherent sheaves on (Q) are related via the full and faithful functor – kQ L U.  相似文献   

11.
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   

12.
In this work we show that a directed translation quiver such that every path from a injective vertex to a projective vertex that has at most two hooks and in case two, they are consecutives, can be embedded in a quiver . This generalizes a result by (Li, Comm. Algebra, 28(10),4635–4645, 2000). Dedicated to Raymundo Bautista on his 60th Birthday.  相似文献   

13.
利用quiver方法确定了一个广义Taft代数具有拟三角Hopf结构当且仅当它是Sweedler 4维Hopf代数.用不同于文[15]的方法,对任意的正整数n,构造出一类拟三角Hopf代数H(n).  相似文献   

14.
Yu-Han Liu 《代数通讯》2013,41(8):3013-3031
We compute Balmer's prime spectrum for the derived category of quiver representations for a finite ordered quiver with the vertex-wise tensor product and show that it does not recover the quiver. We then associate an algebra to every k-linear triangulated tensor category and show that the path algebra can be recovered in this way.  相似文献   

15.
Semisimple Representations of Quivers in Characteristic p   总被引:1,自引:0,他引:1  
We prove that the results of Le Bruyn and Procesi on the varieties parameterizing semisimple representations of quivers hold over an algebraically closed base field of arbitrary characteristic.  相似文献   

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带有关系箭图的路余代数在余代数理论研究中起着重要作用.研究带有关系的路余代数,得到了一个有趣的结果,这对余代数结构的研究会有所裨益.  相似文献   

18.
A symmetric quiver (Q, σ) is a finite quiver without oriented cycles Q?=?(Q 0, Q 1) equipped with a contravariant involution σ on $Q_0\sqcup Q_1$ . The involution allows us to define a nondegenerate bilinear form $\langle -,-\rangle_V$ on a representation V of Q. We shall say that V is orthogonal if $\langle -,-\rangle_V$ is symmetric and symplectic if $\langle -,-\rangle_V$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if (Q, σ) is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type c V and, when the matrix defining c V is skew-symmetric, by the Pfaffians pf V . To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector.  相似文献   

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Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds to a tilting object in the cluster category. The cluster tilted algebra is the algebra of endomorphisms of that tilting object. Viewing the cluster tilted algebra as a path algebra of a quiver with relations, we prove in this paper that the quiver of the cluster tilted algebra is equal to the cluster diagram. We study also the relations. As an application of these results, we answer several conjectures on the connection between cluster algebras and quiver representations.Presented by V. Dlab.  相似文献   

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