منابع مشابه
Koszul and Gorenstein properties for homogeneous algebras
Koszul property was generalized to homogeneous algebras of degree N > 2 in [5], and related to N -complexes in [7]. We show that if the N -homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem [23] to A, i.e., there is a Poincaré duality between Hochschild homology and cohomology of A, as for N = 2. Mathem...
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From symplectic reflection algebras [12], some algebras are naturally introduced. We show that these algebras are non-homogeneous N Koszul algebras. The Koszul property was generalized to homogeneous algebras of degree N > 2 in [6]. In the present paper, the extension of the Koszul property to non-homogeneous algebras is realized through a PBW theorem. This PBW theorem is the generalization to ...
متن کاملGerasimov's Theorem and N -koszul Algebras
This paper 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 due to Gerasimov. As a consequence of the criterion, some new examples of N-Koszul algebras are presented. We give an alternative proof of Gerasimov’s theorem for N = 2, which is related to Dubois-Violette’...
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The study of Koszul algebras and their representations has accelerated significantly in the last few years. They have been used in Topology, Algebraic Geometry and Commutative Algebra and they are used more and more frequently in Representation Theory, see for instance [BGS],[GTM],[M],[MZ] and [R]. The aim of this paper is to present some of the results presented by the second author at the Lum...
متن کامل1 Koszul Algebras
The algebras Qn describe the relationship between the roots and coefficients of a non-commutative polynomial. I.Gelfand, S.Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this work we find the Hilbert series of the class of algebras corresponding to the n-vertex path, Pn. We also show this algebra is Koszul. We do this by first looking at class of qua...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.10.031