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Related papers: Extensions of Verma modules

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In this paper we classify degenerate Verma modules over the linearly compact Lie superalgebra $E(4,4)$. This completes the description of Verma modules over the exceptional linearly compact Lie superalgebras. As in the other cases all…

Representation Theory · Mathematics 2026-03-18 Nicoletta Cantarini , Fabrizio Caselli , Victor Kac

We categorify Verma and indecomposable projective modules in the category $\mathcal I_{\mathfrak{g}}(\mathfrak{sl}_2)$ for $\mathfrak{sl}_2$ using a tensor product decomposition theorem of T. J. Enright and work of J. Chuang and R.…

Representation Theory · Mathematics 2018-06-11 Ben Cox , Mee Seong Im

In this paper, we study extensions between two finite irreducible conformal modules over the Schr\"odinger-Virasoro conformal algebra and the extended Schr\"odinger-Virasoro conformal algebra. Also, we classify all finite nontrivial…

Rings and Algebras · Mathematics 2019-07-08 Lamei Yuan , Kaijing Ling

We compute the algebras of self-extensions of the vacuum module and the Verma modules over an affine Kac-Moody algebra g^ in suitable categories of Harish-Chandra modules. We show that at the critical level these algebras are isomorphic to…

Quantum Algebra · Mathematics 2007-05-23 Edward Frenkel , Constantin Teleman

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…

Category Theory · Mathematics 2015-03-17 Nguyen Tien Quang

In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended…

Quantum Algebra · Mathematics 2007-05-23 Hiroshi Yamauchi

We give a functorial characterization of Mittag-Leffler modules and strict Mittag-Leffler modules.

Commutative Algebra · Mathematics 2017-07-12 Carlos Sancho , Fernando Sancho , Pedro Sancho

The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.

Quantum Algebra · Mathematics 2012-11-14 Chongying Dong , Xiangyu Jiao , Feng Xu

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.

Category Theory · Mathematics 2009-05-21 Roman Mikhailov , Inder Bir S. Passi

Memoir on the Sigma invariants and their applications, version 2

Group Theory · Mathematics 2013-03-04 Ralph Strebel

A practical method for constructing a nontrivial homomorphsim between Verma modules is described.

Representation Theory · Mathematics 2007-05-23 W. A. de Graaf

We improve the previuosly known bound for some vertex Folkman numbers.

Combinatorics · Mathematics 2007-05-23 N. Kolev , N. Nenov

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the…

Representation Theory · Mathematics 2015-02-26 Libor Křižka , Petr Somberg

A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules…

Representation Theory · Mathematics 2025-06-25 Yaohui Xue , Yan Wang

We characterize Gorenstein modules over those local rings that admit a finite contracting endomorphism.

Commutative Algebra · Mathematics 2007-10-01 Hamid Rahmati

In this paper, mirror extensions of vertex operator algebras is considered via tensor categories. The mirror extension conjecture is proved.

Quantum Algebra · Mathematics 2015-06-11 Xingjun Lin

In this paper we define the degree of a morphism between (generalized) Verma modules over a graded Lie superalgebra and construct series of morphisms of various degrees between (generalized) Verma modules over the exceptional…

Mathematical Physics · Physics 2010-03-09 Alexei Rudakov

We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all…

Representation Theory · Mathematics 2015-02-25 Kevin Coulembier , Volodymyr Mazorchuk

In this paper, we consider subcategories consisting of the extensions of modules in two given Serre subcategories to find a method of constructing Serre subcategories of the category of modules. We shall give a criterion for this…

Commutative Algebra · Mathematics 2011-03-09 Takeshi Yoshizawa

For any additive subgroup $G$ of an arbitrary field $F$ of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra $L[G]$. Given a total order of $G$ compatible with its group structure, and any…

Quantum Algebra · Mathematics 2007-05-23 Ran Shen , Yucai Su