摘要 :
The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly...
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The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly Koszul-like module if and only if it can be approximated by Koszul-like graded submodules, which is equivalent to the fact that G(M) is a Koszul-like module, where G(M) denotes the associated graded module of M. As applications, the relationships between minimal graded projective resolutions of M and G(M), and Koszul-like submodules are established. Moreover, the Koszul dual of a weakly Koszul-like module is proved to be generated in degree 0 as a graded E(A) -module.
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In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of ...
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In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary and sufficient conditions for ΚL(A) = L(A) are provided, where ΚL(A) and L(A) denote the categories of Koszul-like modules and modules with linear presentations (see [1]-[3], etc.) respectively, and A is a Koszul-like algebra. We construct new Koszul-like algebras from the known ones by the "one-point extension." Some criteria for a graded algebra to be Koszul-like are provided. Finally, we construct many classical Koszul objects from the given Koszul-like objects.
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Let A = circle plus i >= 0 A(i) be a piecewise-Koszul algebra with cohomology degree function delta(d)(p) such that d > p >= 2 and E(A) = circle plus(i >= 0) Ext(A)(i) (A(0), A(0)) its Yoneda algebra. We introduce a new grading on E(A):
摘要 :
We study the quadratic algebras in Artin-Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that . All the algebras obtained are proved to be Koszul algebras or piecewise-Koszul algebras. In additi...
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We study the quadratic algebras in Artin-Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that . All the algebras obtained are proved to be Koszul algebras or piecewise-Koszul algebras. In addition, we find that there don't exist d-Koszul (d > 2) Artin-Schelter regular algebras of dimension 5.
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We discuss certain homological properties of graded algebras whose trivial modules admit nonpure resolutions. Such algebras include both of Artin-Schelter regular algebras of types (12221) and (13431). Under certain conditions, a ...
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We discuss certain homological properties of graded algebras whose trivial modules admit nonpure resolutions. Such algebras include both of Artin-Schelter regular algebras of types (12221) and (13431). Under certain conditions, a module with nonpure resolution is decomposed to form an extension by two modules with pure resolutions.
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The piecewise-Koszul algebras are generalizations of classical Koszul and higher Koszul algebras. We give a criterion for a connected graded algebra A to be a piecewise-Koszul algebra in terms of an A(infinity)-algebra structure o...
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The piecewise-Koszul algebras are generalizations of classical Koszul and higher Koszul algebras. We give a criterion for a connected graded algebra A to be a piecewise-Koszul algebra in terms of an A(infinity)-algebra structure on its Koszul dual.
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摘要 :The main purpose of this paper is to provide some new criteria for a standard graded algebra A = ⊕ i≥0 A i to be a λ-Koszul algebra, which was first introduced in [12] and was another class of “Koszul-type” algebras includin...
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The main purpose of this paper is to provide some new criteria for a standard graded algebra A = ⊕ i≥0 A i to be a λ-Koszul algebra, which was first introduced in [12] and was another class of “Koszul-type” algebras including Koszul and d-Koszul algebras as special examples.
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The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symm...
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The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symmetric special biserial algebras in terms of quivers and relations.
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In this paper, we mainly focus on the Poincare-Birkhoff-Witt (PBW) deformation theory for a class of N-homogeneous algebras; here N >= 2 is an integer, which generalizes the results in [2] and [7]. More precisely, let k be a field...
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In this paper, we mainly focus on the Poincare-Birkhoff-Witt (PBW) deformation theory for a class of N-homogeneous algebras; here N >= 2 is an integer, which generalizes the results in [2] and [7]. More precisely, let k be a field of characteristic zero, V a finite dimensional vector space over k, and A = T(V)/(R) an N-homogeneous algebra (i.e., R subset of V-circle times N) with Tor(A)(3)(k, k) being supported in a single degree d such that d > N. Set F-n := circle plus(0 = 0 and J(n) = 0 for n < N.
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In this paper we generalize the Koszul complexes and Koszul algebras, and introduce the higher Koszul (t-Koszul) complexes and higher Koszul algebras, where t ≥ 2 is an integer. We prove that an algebra is t-Koszul if and only if...
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In this paper we generalize the Koszul complexes and Koszul algebras, and introduce the higher Koszul (t-Koszul) complexes and higher Koszul algebras, where t ≥ 2 is an integer. We prove that an algebra is t-Koszul if and only if its t-Koszul complex is augmented, i.e. the higher degree (≥ 1) homologies vanish. For arbitrary t-Koszul algebra Λ, we also give a description of the structure of the cohomology algebra Ext_Λ~· (Λ_0, Λ_0) by using the t-Koszul complexes, where the Λ_0 is the direct sum of the simples.
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