Displaying similar documents to “Some Results About Holonomic ε -Modules”

Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

Similarity:

Let U be a dg- A -module, B the endomorphism dg-algebra of U . We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories 𝐃 ( C , d ) of C , 𝐃 ( B , d ) of B and 𝐃 ( A , d ) of A . We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained....

On the composition structure of the twisted Verma modules for 𝔰𝔩 ( 3 , )

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

Similarity:

We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra 𝔰𝔩 ( 3 , ) , including the explicit structure of singular vectors for both 𝔰𝔩 ( 3 , ) and one of its Lie subalgebras 𝔰𝔩 ( 2 , ) , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as D -modules on the Schubert cells in the full flag manifold for SL ( 3 , ) .

Separable k -free modules with almost trivial dual

Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

An R -module M has an almost trivial dual if there are no epimorphisms from M to the free R -module of countable infinite rank R ( ω ) . For every natural number k > 1 , we construct arbitrarily large separable k -free R -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.

Lifting D -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

Similarity:

We study liftings or deformations of D -modules ( D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic D -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given D -module in positive characteristic. At the end we compare...

Relative tilting modules with respect to a semidualizing module

Maryam Salimi (2019)

Czechoslovak Mathematical Journal

Similarity:

Let R be a commutative Noetherian ring, and let C be a semidualizing R -module. The notion of C -tilting R -modules is introduced as the relative setting of the notion of tilting R -modules with respect to C . Some properties of tilting and C -tilting modules and the relations between them are mentioned. It is shown that every finitely generated C -tilting R -module is C -projective. Finally, we investigate some kernel subcategories related to C -tilting modules.

Category 𝒪 for quantum groups

Henning Haahr Andersen, Volodymyr Mazorchuk (2015)

Journal of the European Mathematical Society

Similarity:

In this paper we study the BGG-categories 𝒪 q associated to quantum groups. We prove that many properties of the ordinary BGG-category 𝒪 for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for 𝒪 and for finite dimensional U q -modules we are able...

Melkersson condition on Serre subcategories

Reza Sazeedeh, Rasul Rasuli (2016)

Colloquium Mathematicae

Similarity:

Let R be a commutative noetherian ring, let be an ideal of R, and let be a subcategory of the category of R-modules. The condition C , defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to belong to . In this paper, we define and study the class consisting of all modules satisfying C . If and are ideals of R, we get a necessary and sufficient condition for to satisfy C and C simultaneously. We also...

On τ -extending modules

Y. Talebi, R. Mohammadi (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper we introduce the concept of τ -extending modules by τ -rational submodules and study some properties of such modules. It is shown that the set of all τ -rational left ideals of R R is a Gabriel filter. An R -module M is called τ -extending if every submodule of M is τ -rational in a direct summand of M . It is proved that M is τ -extending if and only if M = R e j M E ( R / τ ( R ) ) N , such that N is a τ -extending submodule of M . An example is given to show that the direct sum of τ -extending modules need not...

A note on generalizations of semisimple modules

Engin Kaynar, Burcu N. Türkmen, Ergül Türkmen (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A left module M over an arbitrary ring is called an ℛ𝒟 -module (or an ℛ𝒮 -module) if every submodule N of M with Rad ( M ) N is a direct summand of (a supplement in, respectively) M . In this paper, we investigate the various properties of ℛ𝒟 -modules and ℛ𝒮 -modules. We prove that M is an ℛ𝒟 -module if and only if M = Rad ( M ) X , where X is semisimple. We show that a finitely generated ℛ𝒮 -module is semisimple. This gives us the characterization of semisimple rings in terms of ℛ𝒮 -modules. We completely determine the structure...

Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour (2022)

Czechoslovak Mathematical Journal

Similarity:

Let I be an ideal of a commutative Noetherian ring R . It is shown that the R -modules H I j ( M ) are I -cofinite for all finitely generated R -modules M and all j 0 if and only if the R -modules Ext R i ( N , H I j ( M ) ) and Tor i R ( N , H I j ( M ) ) are I -cofinite for all finitely generated R -modules M , N and all integers i , j 0 .

A note on Frobenius divided modules in mixed characteristics

Pierre Berthelot (2012)

Bulletin de la Société Mathématique de France

Similarity:

If X is a smooth scheme over a perfect field of characteristic p , and if 𝒟 X ( ) is the sheaf of differential operators on X [7], it is well known that giving an action of 𝒟 X ( ) on an 𝒪 X -module is equivalent to giving an infinite sequence of 𝒪 X -modules descending via the iterates of the Frobenius endomorphism of X [5]. We show that this result can be generalized to any infinitesimal deformation f : X S of a smooth morphism in characteristic p , endowed with Frobenius liftings. We also show that it...

Stratified modules over an extension algebra

Erzsébet Lukács, András Magyar (2018)

Czechoslovak Mathematical Journal

Similarity:

Let A be a standard Koszul standardly stratified algebra and X an A -module. The paper investigates conditions which imply that the module Ext A * ( X ) over the Yoneda extension algebra A * is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.

Weak n -injective and weak n -fat modules

Umamaheswaran Arunachalam, Saravanan Raja, Selvaraj Chelliah, Joseph Kennedy Annadevasahaya Mani (2022)

Czechoslovak Mathematical Journal

Similarity:

We introduce and study the concepts of weak n -injective and weak n -flat modules in terms of super finitely presented modules whose projective dimension is at most n , which generalize the n -FP-injective and n -flat modules. We show that the class of all weak n -injective R -modules is injectively resolving, whereas that of weak n -flat right R -modules is projectively resolving and the class of weak n -injective (or weak n -flat) modules together with its left (or right) orthogonal class forms...

Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang, Xiaoming Li (2023)

Czechoslovak Mathematical Journal

Similarity:

Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.