共查询到20条相似文献,搜索用时 15 毫秒
1.
Edward L. Green 《代数通讯》2013,41(11):4033-4054
This paper continues the study of n-full graphs and their connection to certain Koszul algebras started in Green and Hartman (to appear). We provide constructive methods for creating new full graphs from old and study the associated Koszul algebras and the projective resolution of simple modules over such algebras. 相似文献
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D. I. Piontkovskii 《Functional Analysis and Its Applications》2005,39(2):120-130
We study associative graded algebras that have a “complete flag” of cyclic modules with linear free resolutions, i.e., algebras over which there exist cyclic Koszul modules with any possible number of relations (from zero to the number of generators of the algebra). Commutative algebras with this property were studied in several papers by Conca and others. Here we present a noncommutative version of their construction.We introduce and study the notion of Koszul filtration in a noncommutative algebra and examine its connections with Koszul algebras and algebras with quadratic Grobner bases. We consider several examples, including monomial algebras, initially Koszul algebras, generic algebras, and algebras with one quadratic relation. It is shown that every algebra with a Koszul filtration has a rational Hilbert series.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 47–60, 2005Original Russian Text Copyright © by D. I. PiontkovskiiSupported in part by the Russian Foundation for Basis Research under project 02-01-00468. 相似文献
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The concept of Koszul differential graded (DG for short) algebra is introduced in [8]. Let A be a Koszul DG algebra. If the Ext-algebra of A is finite-dimensional, i.e., the trivial module Ak is a compact object in the derived category of DG A-modules, then it is shown in [8] that A has many nice properties. However, if the Ext-algebra is infinite-dimensional, little is known about A. As shown in [15] (see also Proposition 2.2), Ak is not compact if H(A) is finite-dimensional. In this paper, it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality. A DG version of the BGG correspondence is deduced from the Koszul duality theorem. 相似文献
5.
Amir Hashemi Benyamin M.-Alizadeh Mahdi Dehghani Darmian 《Linear and Multilinear Algebra》2013,61(2):265-272
In this article, we study the minimal polynomials of parametric matrices. Using the concept of (comprehensive) Gröbner systems for parametric ideals, we introduce the notion of a minimal polynomial system for a parametric matrix, i.e. we decompose the space of parameters into a finite set of cells and for each cell we give the corresponding minimal polynomial of the matrix. We also present an algorithm for computing a minimal polynomial system for a given parametric matrix. 相似文献
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With a simple graph G on [n], we associate a binomial ideal PG generated by diagonal minors of an n × n matrix X = (xij) of variables. We show that for any graph G, PG is a prime complete intersection ideal and determine the divisor class group of K[X]/PG. By using these ideals, one may find a normal domain with free divisor class group of any given rank. 相似文献
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一类特殊的Koszul Calabi-Yau DG代数 总被引:1,自引:0,他引:1
假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数. 相似文献
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Jin Yun GUO Quan Hong WAN Qiu Xian WU 《数学学报(英文版)》2007,23(11):1967-1984
We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra. 相似文献
10.
Sheila Brenner Michael C. R. Butler Alastair D. King 《Algebras and Representation Theory》2002,5(4):331-368
The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such almost Koszul algebras is developed and other examples are given. 相似文献
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Kei-ichiro Iima 《代数通讯》2013,41(10):3424-3437
We develop the theory of Gröbner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-to-one correspondences among various sets of partitions by using the division algorithm. 相似文献
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《代数通讯》2013,41(11):4831-4851
Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give sufficient and necessary conditions on a set Θ of non-commutative polynomials to assure that the set G ○ Θ of composed polynomials is a Gröbner basis in the free associative algebra whenever G is. The subject was initiated by Hong, treating the commutative analogue in (1998, J. Symb. Comput. 25, 643–663). 相似文献
14.
Thomas Cassidy 《代数通讯》2013,41(9):3742-3752
Vatne [13] and Green and Marcos [9] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees. 相似文献
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Erik Hillgarter Ralf Hemmecke Günter Landsmann Franz Winkler 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(2):123-147
Differential problems are ubiquitous in mathematical modeling of physical and scientific problems. Algebraic analysis of differential systems can help in determining qualitative and quantitative properties of solutions of such systems. In this tutorial paper we describe several algebraic methods for investigating differential systems. 相似文献
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Pavel Kolesnikov 《代数通讯》2017,45(12):5283-5296
We develop Gröbner–Shirshov bases technique for pre-associative (dendriform) algebras and prove a version of composition-diamond lemma. 相似文献
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Christian Böhning 《代数通讯》2013,41(6):2014-2022
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In this paper, by using Gröbner–Shirshov bases theories, we prove that each countably generated associative algebra (Lie algebra) can be embedded into a simple two-generated associative algebra (Lie algebra). 相似文献
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Lutz Hille 《Mathematische Nachrichten》1998,191(1):189-195
Let G be a reductive algebraic group defined over an algebraically closed field of characteristic zero and let P be a parabolic subgroup of G. We consider the category of homogeneous vector bundles over the flag variety G/P. This category is equivalent to a category of representations of a certain infinite quiver with relations by a generalisation of a result in [BK]. We prove that both categories are Koszul precisely when the unipotent radical Pu of P is abelian. 相似文献
20.
Let A be a brace algebra. This structure implies that A is also a pre-Lie algebra. In this paper, we establish Composition-Diamond lemma for brace algebras. For each pre-Lie algebra L, we find a Gröbner–Shirshov basis for its universal brace algebra Ub(L). As applications, we determine an explicit linear basis for Ub(L) and prove that L is a pre-Lie subalgebra of Ub(L). 相似文献