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91.
We establish a bound on the number of simple and projective modules in the quasi-tubes of the Auslander–Reiten quivers of finite dimensional self-injective algebras over a field. 相似文献
92.
In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras. 相似文献
93.
94.
We study Auslander–Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First, we give a number of combinatorial characterizations of almost acyclic Auslander–Reiten components. Then, we shall show that an Auslander–Reiten component with bounded short cycles is obtained, roughly speaking, by gluing the connecting components of finitely many tilted quotient algebras. In particular, the number of such components is finite and each of them is almost acyclic with only finitely many DTr-orbits. As an application, we show that an artin algebra is representation-finite if and only if its module category has bounded short cycles. This includes a well known result of Ringel’s, saying that a representation-directed algebra is representation-finite. 相似文献
95.
Let E be an equivalence relation on the powerset of an uncountable set, which is reasonably definable. We assume that any two subsets with symmetric difference of size exactly 1 are not equivalent. We investigate whether for E there are many pairwise non equivalent sets.
I would like to thank Alice Leonhardt for the beautiful typing.This research was supported by The Israel Science Foundation. Publication 724.
Mathematics Subject Classification (2000): 03E47, 03E35; 20K20, 20K35 相似文献
96.
97.
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
98.
We study the relationship between representation theoretic properties and homological properties of orders. We show that there
is a close relationship among Auslander orders, τ-categories and Auslander regular rings. As an application, we give a combinatorial
characterization of finite Auslander–Reiten quivers of orders.
Presented by K. Roggenkamp
Mathematics Subject Classifications (2000) Primary: 16G30; secondary: 16E65, 16G70, 18E05.
Current address: Department of Mathematics, University of Hyogo, Himeji, 671-2201, Japan. e-mail: iyama@sci.u-hyogo.ac.jp 相似文献
99.
本文利用exactBorel子代数刻划了遗传代数,给出了basic拟遗传代数的主子代数是exactBorel子代数的充分必要条件. 相似文献
100.
José L. Bueso J. Gómez-Torrecillas F. J. Lobillo 《Algebras and Representation Theory》2001,4(3):201-218
In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Ext
i
(M,N) is provided when N is a centralizing bimodule. 相似文献