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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):
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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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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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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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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, the notions of nonpure piecewise-Koszul algebra and nonpure piecewise-Koszul module are introduced, which are the “nonpure” version of piecewise-Koszul algebras and modules first introduced in [19]. Some criteria ...
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In this paper, the notions of nonpure piecewise-Koszul algebra and nonpure piecewise-Koszul module are introduced, which are the “nonpure” version of piecewise-Koszul algebras and modules first introduced in [19]. Some criteria for a standard graded algebra to be nonpure piecewise-Koszul are given. We also discuss some basic properties of nonpure piecewise-Koszul modules. Further more, we give a sufficient condition for the questions raised in [20] to be true in terms of nonpure piecewise-Koszul modules.
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The concept of (strongly) weakly piecewise-Koszul module is in-troduced. Let A be a piecewise-Koszul algebra. Then M E WP(A) if andonly if M admits a tower of piecewise-Koszul modules. As applications of theapproximation chain, we...
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The concept of (strongly) weakly piecewise-Koszul module is in-troduced. Let A be a piecewise-Koszul algebra. Then M E WP(A) if andonly if M admits a tower of piecewise-Koszul modules. As applications of theapproximation chain, we show that the finitistic dimension conjecture is truein WP(A) in a special case and for M ∈ WP(A) or SWP(A), the Koszuldual ε(M) ∈ gro(E(A)). In particular, if M ∈ P(A), then M ∈ SWP(A) ifand only if ε(M) ∈ gro(E(A)). Furthermore, we show that M ∈ WP(A) ifand only if ε(G(M)) ∈ gr0(E(A)).
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We provide a class of Artin-Schelter regular algebras of global dimension 5 with four generators, which is obtained by parametrizing a finite-dimensional graded Lie algebra. Moreover, the algebras are piecewise-Koszul under a slig...
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We provide a class of Artin-Schelter regular algebras of global dimension 5 with four generators, which is obtained by parametrizing a finite-dimensional graded Lie algebra. Moreover, the algebras are piecewise-Koszul under a slight constraint on the parameters.
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The main aim of this article is to discuss the piecewise-Koszul property of finitely generated modules in the nongraded case. In particular, the notion of quasi-piecewise-Koszul module, a natural extension of quasi-Koszul modules ...
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The main aim of this article is to discuss the piecewise-Koszul property of finitely generated modules in the nongraded case. In particular, the notion of quasi-piecewise-Koszul module, a natural extension of quasi-Koszul modules (see [2]), quasi-d-Koszul modules (see [12] or [6]) and piecewise-Koszul modules (see [7]), is introduced. Let R be a Noetherian semiperfect algebra with Jacobson radical J and M a finitely generated R-module. The structure of the graded E(R) = ? _(i≥0) Ext _R ~i(R/J, R/J)-module E(M) = ? _(i≥0) Ext _r ~i(M, R/J) is studied in detail and some necessary and sufficient conditions for a finitely generated R-module to be quasi-piecewise-Koszul are provided. Moreover, as an application of quasi-piecewise-Koszul modules, we give a necessary and sufficient condition for the minimal Horseshoe Lemma to be true in the category of quasi-piecewise-Koszul modules, which perfects Theorem 2.8 of [13] and Theorem 3.1 of [9]. Finally, some applications of the minimal Horseshoe Lemma are also given.
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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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