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Displaying similar documents to “Some properties of generalized reduced Verma modules over -graded modular Lie superalgebras”

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

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

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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 , ) .

Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki, Rachid Tribak (2023)

Czechoslovak Mathematical Journal

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We provide some characterizations of rings R for which every (finitely generated) module belonging to a class 𝒞 of R -modules is a direct sum of cyclic submodules. We focus on the cases, where the class 𝒞 is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

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We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between n -Gorenstein star modules and n -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of n -Gorenstein tilting modules.

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

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We construct a family of non-weight modules which are free U ( 𝔥 ) -modules of rank 2 over the N = 1 super Schrödinger algebra in ( 1 + 1 ) -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free U ( 𝔥 ) -modules of rank 2 over 𝔬𝔰𝔭 ( 1 | 2 ) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

Category 𝒪 for quantum groups

Henning Haahr Andersen, Volodymyr Mazorchuk (2015)

Journal of the European Mathematical Society

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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...

Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions

Adrien Deloro (2013)

Confluentes Mathematici

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We classify quadratic SL 2 ( 𝕂 ) - and 𝔰𝔩 2 ( 𝕂 ) -modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.

Top-stable and layer-stable degenerations and hom-order

S. O. Smalø, A. Valenta (2007)

Colloquium Mathematicae

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Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration M < d e g N such that t M / t + 1 M t N / t + 1 N for all t. Given a module M with square-free top and a projective cover P, she showed that d i m k H o m ( M , M ) = d i m k H o m ( P , M ) if and only if M has no proper degeneration M < d e g N where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from...

n -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

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Let R be a graded ring and n 1 an integer. We introduce and study n -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever n > m . Many properties of the n -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized....

Branching problems and 𝔰𝔩 ( 2 , ) -actions

Pavle Pandžić, Petr Somberg (2015)

Archivum Mathematicum

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We study certain 𝔰𝔩 ( 2 , ) -actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs ( 𝔤 , 𝔭 ) , ( 𝔤 ' , 𝔭 ' ) of Lie algebras and their parabolic subalgebras.

Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

Jon F. Carlson, Nadia Mazza, Jacques Thévenaz (2013)

Journal of the European Mathematical Society

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Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial k G -modules, whose restrictions to P are isomorphic to the direct sum of the known exotic endotrivial k P -modules and some projective modules. This provides a description of the group T ( G ) of endotrivial k G -modules.

Separable functors for the category of Doi Hom-Hopf modules

Shuangjian Guo, Xiaohui Zhang (2016)

Colloquium Mathematicae

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Let ̃ ( k ) ( H ) A C be the category of Doi Hom-Hopf modules, ̃ ( k ) A be the category of A-Hom-modules, and F be the forgetful functor from ̃ ( k ) ( H ) A C to ̃ ( k ) A . The aim of this paper is to give a necessary and suffcient condition for F to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.

A cluster algebra approach to q -characters of Kirillov–Reshetikhin modules

David Hernandez, Bernard Leclerc (2016)

Journal of the European Mathematical Society

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We describe a cluster algebra algorithm for calculating q -characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra U q ( 𝔤 ^ ) . This yields a geometric q -character formula for tensor products of Kirillov–Reshetikhin modules. When 𝔤 is of type A , D , E , this formula extends Nakajima’s formula for q -characters of standard modules in terms of homology of graded quiver varieties.