共查询到20条相似文献,搜索用时 15 毫秒
1.
Edward L. Green Gregory Hartman Eduardo N. Marcos Øyvind Solberg 《Archiv der Mathematik》2005,85(2):118-127
In this paper we show that if
is a Koszul algebra with Λ0 isomorphic to a product of copies of a field, then the minimal projective resolution of Λ0 as a right Λ-module provides all the information necessary to construct both a minimal projective resolution of Λ0 as a left Λ-module and a minimal projective resolution of Λ as a right module over the enveloping algebra of Λ. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of Λ0 as a right Λ-module.Received: 14 September 2004 相似文献
2.
《Journal of Pure and Applied Algebra》2023,227(3):107208
We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson n-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras using curved Koszul duality. We use these resolutions to compute derived enveloping algebras and factorization homology on parallelized simply connected closed manifolds with coefficients in these Poisson n-algebras. 相似文献
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4.
Vyjayanthi Chari 《Advances in Mathematics》2009,220(4):1193-328
Let g be a finite-dimensional simple Lie algebra and let Sg be the locally finite part of the algebra of invariants (EndCV⊗Sg(g)) where V is the direct sum of all simple finite-dimensional modules for g and S(g) is the symmetric algebra of g. Given an integral weight ξ, let Ψ=Ψ(ξ) be the subset of roots which have maximal scalar product with ξ. Given a dominant integral weight λ and ξ such that Ψ is a subset of the positive roots we construct a finite-dimensional subalgebra of Sg and prove that the algebra is Koszul of global dimension at most the cardinality of Ψ. Using this we construct naturally an infinite-dimensional non-commutative Koszul algebra of global dimension equal to the cardinality of Ψ. The results and the methods are motivated by the study of the category of finite-dimensional representations of the affine and quantum affine algebras. 相似文献
5.
For affine toric varieties X and defined by dual cones, we define an equivalence of categories between mixed versions of the equivariant derived category and the derived category of sheaves on which are locally constant with unipotent monodromy on each orbit. This equivalence satisfies the Koszul duality formalism of Beilinson, Ginzburg, and Soergel. 相似文献
6.
Kohji Yanagawa 《Journal of Pure and Applied Algebra》2006,207(1):77-97
Let A be a noetherian AS-regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and the category of finitely generated graded left A-modules. Following Jørgensen, we define the Castelnuovo-Mumford regularity of a complex in terms of the local cohomologies or the minimal projective resolution of M•. Let A! be the quadratic dual ring of A. For the Koszul duality functor , we have . Using these concepts, we interpret results of Martinez-Villa and Zacharia concerning weakly Koszul modules (also called componentwise linear modules) over A!. As an application, refining a result of Herzog and Römer, we show that if J is a monomial ideal of an exterior algebra E=?〈y1,…,yd〉, d≥3, then the (d−2)nd syzygy of E/J is weakly Koszul. 相似文献
7.
We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property. 相似文献
8.
Let A and B be algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that T is Koszul if and only if both A and B are Koszul. Furthermore, we prove that an algebra is Koszul if and only if one of its iterated dual extension algebras is Koszul, if and only if all its iterated dual extension algebras are Koszul. Finally, we give a necessary and sufficient condition for a dual extension algebra to have the property that all linearly presented modules are Koszul modules, which provides an effective way to construct algebras with such a property. 相似文献
9.
Dag Oskar Madsen 《Advances in Mathematics》2011,(6):2327
We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. 相似文献
10.
The Koszul property was generalized to homogeneous algebras of degree in [5], and related to -complexes. We show that if the -homogeneous algebra is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem to i.e., there is a Poincaré duality between Hochschild homology and cohomology of as for . 相似文献
11.
Thomas Cassidy 《Journal of Pure and Applied Algebra》2010,214(7):1011-1016
Green and Marcos (2005) [2] call a graded k-algebra δ-Koszul if the corresponding Yoneda algebra is finitely generated and there exists a function δ:N→N such that is zero if j≠δ(i). For any integer m≥3 we exhibit a noncommutative quadratic δ-Koszul algebra for which the Yoneda algebra is generated in degrees (1,1) and (m,m+1). These examples answer a question of Green and Marcos. These algebras are not Koszul but m-Koszul (in the sense of Backelin). 相似文献
12.
Motivated by the theory of quasi-determinants, we study non-commutative algebras of quasi-Plücker coordinates. We prove that these algebras provide new examples of non-homogeneous quadratic Koszul algebras by showing that their quadratic duals have quadratic Gröbner bases. 相似文献
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Volodymyr Mazorchuk 《manuscripta mathematica》2010,131(1-2):1-10
We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the class of these algebras is closed with respect to both dualities and that on this class these two dualities commute. All arguments reduce to short computations in the bounded derived category of graded modules. 相似文献
15.
Jonas T. Hartwig 《Journal of Pure and Applied Algebra》2011,215(10):2352-2377
We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coefficient ring R), which is assumed to carry an involution of the form X∗=Y, R∗⊆R. We prove that a weight module V is pseudo-unitarizable iff it is isomorphic to its finitistic dual V?. Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necessary and sufficient conditions for an indecomposable weight module to be isomorphic to its finitistic dual, and thus to be pseudo-unitarizable. Some examples are given, including Uq(sl2) for q a root of unity. 相似文献
16.
The study of maximal-primary irreducible ideals in a commutative graded connected Noetherian algebra over a field is in principle equivalent to the study of the corresponding quotient algebras. Such algebras are Poincaré duality algebras. A prototype for such an algebra is the cohomology with field coefficients of a closed oriented manifold. Topological constructions on closed manifolds often lead to algebraic constructions on Poincaré duality algebras and therefore also on maximal-primary irreducible ideals. It is the purpose of this note to examine several of these and develop some of their basic properties. 相似文献
17.
Motivated by Weyl algebra analogues of the Jacobian conjecture and the tame generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl–Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of . 相似文献
18.
We show that-up to precisely one-each exceptional module over a domestic canonical algebra of quiver type over a field k can be represented by matrices whose entries are just 0 and 1. In the case we calculate the matrices of these representations explicitly. 相似文献
19.
Tom Braden Anthony Licata Nicholas Proudfoot Ben Webster 《Advances in Mathematics》2010,225(4):2002-2049
Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O. 相似文献
20.
With an aim of exploring homological algebra for weak Hopf modules, this paper investigates the HOM-functor and presents the structure theorem for endomorphism algebras of weak two-sided (A,H)-Hopf modules, and gives the duality theorem for weak “big” smash products. 相似文献