共查询到20条相似文献,搜索用时 15 毫秒
1.
Yao Hailou 《数学季刊》1998,(3)
§1. IntroductionLetAbeanartinalgebra,modAbethecategoryoffinitelygeneratedrightA-modules,ΓAbeitsAuslander-Reitenquiver,thenthereisanonzeromapbetweenanytwonon-isomorphicmodulesinmodAifandonlyifthereisapathbetweenthetwoverticescorrespondingtothesetwomod… 相似文献
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Anders Skovsted Buch 《Journal of Algebraic Combinatorics》2001,13(2):151-172
In A.S. Buch and W. Fulton [Invent. Math. 135 (1999), 665–687] a formula for the cohomology class of a quiver variety is proved. This formula writes the cohomology class of a quiver variety as a linear combination of products of Schur polynomials. In the same paper it is conjectured that all of the coefficients in this linear combination are non-negative, and given by a generalized Littlewood-Richardson rule, which states that the coefficients count certain sequences of tableaux called factor sequences. In this paper I prove some special cases of this conjecture. I also prove that the general conjecture follows from a stronger but simpler statement, for which substantial computer evidence has been obtained. Finally I will prove a useful criterion for recognizing factor sequences. 相似文献
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Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the canonical decomposition for quivers with three vertices gives us fractal-like pictures. 相似文献
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Buch and Fulton [9] conjectured the nonnegativity of the quiver coefficients appearing in their formula for a quiver cycle. Knutson, Miller and Shimozono [24] proved this conjecture as an immediate consequence of their component formula. We present an alternative proof of the component formula by substituting combinatorics for Gröbner degeneration [23, 24]. We relate the component formula to the work of Buch, Kresch, Tamvakis and the author [10] where a splitting formula for Schubert polynomials in terms of quiver coefficients was obtained. We prove analogues of this latter result for the type BCD-Schubert polynomials of Billey and Haiman [4]. The form of these analogues indicate that it should be interesting to pursue a geometric context that explains them. 相似文献
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Algebras and Representation Theory - For an acyclic quiver, we establish a connection between the cohomology of quiver Grassmannians and the dual canonical bases of the algebra $U_{q}^{-}(\mathfrak... 相似文献
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在文献[3]和[6]中,Hopf箭图的路代数上的Hopf代数结构和覆盖箭图的路余代数上的Hopf代数结构分别被给出.该文通过一个箭图是Hopf箭图当且仅当它是箭图覆盖这一结论,来讨论同一箭图上给出的这两种Hopf代数结构之间的对偶关系(见定理3和定理4).作为应用,作者先得到关于定向圈的路代数的商上的Hopf代数结构的一些性质,然后证明了Sweedler的4维-Hopf代数小仅是拟三角的而且是余拟三角的.最后,作者刻画了Schurian覆盖箭图的路代数上的Hopf代数的分次自同构群. 相似文献
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Xiao Qin DENG Jiang Rong CHEN 《数学学报(英文版)》2005,21(3):613-622
The notion of generic extensions of representations of a Dynkin quiver plays a big role in the study of the structure of the corresponding quantum group. In this paper, we describe the generic extensions of a simple representation by any representation and that of any representation by a simple representation of a Dynkin quiver Q of type D. 相似文献
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Claudio Somaini 《代数通讯》2013,41(11):4104-4115
Let d be a prehomogeneous dimension vector for a connected quiver Q with the property that c ? d has a negative entry for some ? ∈ ? where c is the Coxeter transformation corresponding to an admissible numbering of the vertices Q 0 of Q. Denote by rep(Q, d) the variety of d-dimensional representations of Q and by Sl(d) the product of the special linear groups at all vertices Q 0. We show how to find the irreducible components of the null cone of the algebraic quotient rep(Q, d)//Sl(d). 相似文献
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Tomohiro Itagaki 《代数通讯》2013,41(8):3472-3497
In this article, we compute the Hochschild homology group of A = KΓ/(f(X s )), where KΓ is the path algebra of the cyclic quiver Γ with s vertices and s arrows over a commutative ring K, f(x) is a monic polynomial over K, and X is the sum of all arrows in KΓ. Moreover, we compute the cyclic homology group of A in the case f(x) = (x ? a) m , where a ∈ K, so that we can determine the cyclic homology of A in general when K is an algebraically closed field. 相似文献
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Christian Wenzel 《Mathematische Nachrichten》1997,187(1):293-310
Let G be a reductive linear algebraic group over an algebraically closed field K, let P? be a parabolic subgroup scheme of G containing a Borel subgroup B, and let P = P?red ? P? be its reduced part. Then P is reduced, a variety, one of the well known classical parabolic subgroups. For char(K) = p > 3, a classification of the P?'s has been given in [W1]. The Chow ring of G/P only depends on the root system of G. Corresponding to the natural projection from G/P to G/P? there is a map of Chow rings from A(G/P?) to A(G/P). This map will be explicitly described here. Let P = B, and let p > 3. A formula for the multiplication of elements in A(G/P?) will be derived. We will prove that A(G/P?) ? A(G/P) (abstractly as rings) if and only if G/P ? G/P? as varieties, i. e., the Chow ring is sensitive to the thickening. Furthermore, in certain cases A(G/P?) is not any more generated by the elements corresponding to codimension one Schubert cells. 相似文献
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An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-injectivity, is investigated. Emphasis is placed on comparing and contrasting the properties of both profiles. In particular, the analog in this context of the notion of poor modules is considered and properties of pure-injectively poor modules are determined. While we do not know of any ring that does not have pure-injectively poor modules, their existence has not been determined in general. Rings having pure-injectively poor modules of various types are characterized. 相似文献
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Let R be a commutative ring with identity, Z(R) its set of zero-divisors, and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is Γ(R) = Z(R)\{0}, with distinct vertices x and y adjacent if and only if xy = 0. In this article, we study Γ(R) for rings R with nonzero zero-divisors which satisfy certain divisibility conditions between elements of R or comparability conditions between ideals or prime ideals of R. These rings include chained rings, rings R whose prime ideals contained in Z(R) are linearly ordered, and rings R such that {0} ≠ Nil(R) ? zR for all z ∈ Z(R)\Nil(R). 相似文献
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Fernando Szechtman 《代数通讯》2013,41(11):4973-4985
Let f(Z) = Zn ? a1Zn?1 + … + (?1)n?1an?1Z + (?1)nan be a monic polynomial with coefficients in a ring R with identity, not necessarily commutative. We study the ideal If of R[X1,…, Xn] generated by σi(X1,…, Xn) ? ai, where σ1,…, σn are the elementary symmetric polynomials, as well as the quotient ring R[X1,…, Xn]/If. 相似文献
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The paper introduces a new grading on the preprojective algebraof an arbitrary locally finite quiver. Viewing the algebra asa left module over the path algebra, the author uses the gradingto give an explicit geometric construction of a canonical collectionof exact sequences of its submodules. If a vertex of the quiveris a source, the above submodules behave nicely with respectto the corresponding reflection functor. It follows that whenthe quiver is finite and without oriented cycles, the canonicalexact sequences are the almost split sequences with preprojectiveterms, and the indecomposable direct summands of the submodulesare the non-isomorphic indecomposable preprojective modules.The proof extends that given by Gelfand and Ponomarev in thecase when the finite quiver is a tree. 2000 Mathematics SubjectClassification 16G10, 16G70. 相似文献
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Let (R, m) be a Noetherian, one-dimensional, local ring, with |R/m|=∞. We study when its associated graded ring G(m) is Buchsbaum; in particular, we give a theoretical characterization for G(m) to be Buchsbaum not Cohen–Macaulay. Finally, we consider the particular case of R being the semigroup ring associated to a numerical semigroup S: we introduce some invariants of S, and we use them in order to give a necessary and a sufficient condition for G(m) to be Buchsbaum. 相似文献
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Julia Sauter 《Algebras and Representation Theory》2017,20(6):1323-1340
Generalizing Schubert cells in type A and a cell decomposition of Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of a cyclic quiver admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation with finitely many fixpoints. As an application of the cell decomposition we obtain a vector space basis of certain modules (for quiver Hecke algebras of nilpotent representations of this quiver), similar modules have been studied by Kato as analogues of standard modules. 相似文献