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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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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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This article is devoted to graded algebras A having a single homogeneous relation. We give a criterion for A to be N-Koszul, where N is the degree of the relation. This criterion uses a theorem of Gerasimov. As a consequence of th...
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This article is devoted to graded algebras A having a single homogeneous relation. We give a criterion for A to be N-Koszul, where N is the degree of the relation. This criterion uses a theorem of Gerasimov. As a consequence of the criterion, some new examples of N-Koszul algebras are presented. We give an alternative proof of Gerasimovs theorem for N = 2, which is related to Dubois-Violettes theorem concerning a matrix description of the Koszul and ASGorenstein algebras of global dimension 2. We determine which of the Poincare–Birkhoff–Witt deformations of a symplectic form are Calabi–Yau.
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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 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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In this paper we study a class of algebras having n-dimensional pyramid shaped quiver with n-cubic cells, which we called n-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic n-Auslander absolu...
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In this paper we study a class of algebras having n-dimensional pyramid shaped quiver with n-cubic cells, which we called n-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic n-Auslander absolutely n-complete algebras introduced by Iyama. We show that the projective resolutions of the simples of n-cubic pyramid algebras can be characterized by n-cuboids, and prove that they are periodic. So these algebras are almost Koszul and (n-1)-translation algebras. We also recover Iyama's cone construction for n-Auslander absolutely n-complete algebras using n-cubic pyramid algebras and the theory of n-translation algebras.
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We extend Koszul calculus defined on quadratic algebras by Berger et al. (2018) [9] to N-homogeneous algebras for any N >= 2, quadratic algebras corresponding to N = 2. We emphasize that N-homogeneous algebras are considered in fu...
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We extend Koszul calculus defined on quadratic algebras by Berger et al. (2018) [9] to N-homogeneous algebras for any N >= 2, quadratic algebras corresponding to N = 2. We emphasize that N-homogeneous algebras are considered in full generality, with no Koszulity assumption. Koszul cup and cap products are introduced and are reduced to usual cup and cap products if N = 2, but if N > 2, they are defined by very specific expressions. These specific expressions are compatible with the Koszul differentials and provide associative products on classes. There is no associativity in general on chainscochains, suggesting that Koszul cochains should constitute an A(infinity)-algebra, acting as an A(infinity)-bimodule on Koszul chains. (C) 2018 Elsevier Inc. All rights reserved.
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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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We study the Jordan triple systems in terms of operads. We give the description of the operad of these ternary algebras as a quadratic operad and prove that the quadratic dual of this operad is the operad of partially antisymmetri...
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We study the Jordan triple systems in terms of operads. We give the description of the operad of these ternary algebras as a quadratic operad and prove that the quadratic dual of this operad is the operad of partially antisymmetric, partially associative ternary algebras. Nous etudions les systemes triples de Jordan en termes d'operades. Nous donnons une description de l'operade quadratique de ces algebres ternaires et montrons que son dual quadratique est l'operade des algebres ternaires partiellement associatives, partiellement antisymetriques. (C) 2000 Academic Press. [References: 15]
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