نتایج جستجو برای: koszul module
تعداد نتایج: 67045 فیلتر نتایج به سال:
The goal of this paper is to provide homological descriptions of monomial ideals. The key concepts in these descriptions are the minimal free resolution, the Koszul homology and the multigraded Betti numbers. These three objects are strongly related, being Tor modules a simple way to describe this relation. We introduce a new tool, Mayer-Vietoris trees which provides a good way to compute the h...
The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra. It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different...
Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of the smash product algebra B#H. Many examples of these deformations are given.
A squarefree module over a polynomial ring S = k[x1, . . . , xn] is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals more systematically. The category Sq of squarefree modules is equivalent to the category of finitely generated left Λ-modules, where Λ is the incidence algebra of the Boolean lattice 2. The derived category D(S...
This article should be viewed as a survey of generalized Koszul complexes and Koszul bicomplexes with an application to generalized Koszul complexes in projective dimension one. We shall try to give detailed information on the basic definitions and a summary of the main results. Concerning proofs the reader is invited to have a look into [I] or [IV]. Introduction. We start with the following qu...
Let Λ be a finite-dimensional (D, A)-stacked monomial algebra. In this paper, we give necessary and sufficient conditions for the variety of a simple Λ-module to be nontrivial. This is then used to give structural information on the algebra Λ, as it is shown that if the variety of every simple module is nontrivial, then Λ is a D-Koszul monomial algebra. We also provide examples of (D, A)-stacke...
In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig’s a-function is formulated (and proved for type A). The second part deals with the extension algebra of Verma modules. I...
The semi-classical data attached to stacks of algebroids in the sense of Kashiwara and Kontsevich are Maurer-Cartan elements on complex manifolds, which we call extended Poisson structures as they generalize holomorphic Poisson structures. A canonical Lie algebroid is associated to each Maurer-Cartan element. We study the geometry underlying these Maurer-Cartan elements in the light of Lie alge...
In this paper we give a criterion for a left Gorenstein algebra to be AS-regular. Let A be a left Gorenstein algebra such that the trivial module Ak admits a finitely generated minimal free resolution. Then A is AS-regular if and only if its left Gorenstein index is equal to− inf{i |ExtA A (k, k)i = 0}. Furthermore, A is Koszul AS-regular if and only if its left Gorenstein index is depthAA = − ...
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