## For all generic q ∈ ℂ*, when $$\mathfrak{g}$$ g is not of type A 1 , we prove that the quantum toroidal algebra $$U_q(\mathfrak{g}_{\rm{tor}})$$ U q ( g t o r ) has no nontrivial finite dimensional simple module.

Finite dimensional modules over quantum toroidal algebras

## The finite-dimensional simple modules over H and K, are classified; they all have dimension 1, respectively $$\le 2$$≤2.

On the bosonization of the super Jordan plane

## We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy.

Classification of some vertex operator algebras of rank 3

## The approach is based on a combination of three simple modules: 1) flood frequency analysis (frequency and peak discharge), 2) estimation of inundation depth, and 3) damage and loss estimation.

Flood risk mapping for direct damage to residential buildings in Quebec, Canada

10.1007/978-3-030-21792-1_5

## We start by describing the Brauer tree, a combinatorial object that encodes first the decomposition matrix of the block, then Ext1 between simple modules in the block, and indeed the Morita equivalence type of the block (but not the source algebra).

Blocks with Cyclic Defect Groups

## We prove the geometric $q$-character formula conjectured by Hernandez and Leclerc in types $\mathbb{A}$ and $\mathbb{B}$ for a class of simple modules called snake modules introduced by Mukhin and Young.

A geometric $q$-character formula for snake modules.

10.1142/s0219498821400016

## Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case $n=2$.

Finite-dimensional Nichols algebras over dual Radford algebras

## In this note, we prove that if $\Lambda$ is an Artin algebra with a simple module $S$ of finite projective dimension, then the finiteness of the finitistic dimension of $\Lambda$ implies that of $(1-e)\Lambda(1-e)$ where $e$ is the primitive idempotent supporting $S$.

Idempotent reduction for the finitistic dimension conjecture

10.1142/s0129167x19500708

## We construct two functors which transform simple restricted modules with nonzero levels over the standard affine algebras into simple modules over the three-point affine algebras of genus zero.

Representations for three-point Lie algebras of genus zero

10.1109/ACCESS.2019.2934718

## Three basic simple modules allows to achieve complex models for a real mine.

On Modelling and Simulating Open Pit Mine Through Stochastic Timed Petri Nets

10.1007/978-3-030-32906-8_3

## In particular, we show the Heisenberg vertex operator algebra gives an example of when the level one Zhu algebra, and in fact all its higher level Zhu algebras, do not provide new indecomposable non simple modules for the vertex operator algebra beyond those detected by the level zero Zhu algebra.

The Level One Zhu Algebra for the Heisenberg Vertex Operator Algebra

10.1007/978-3-030-21792-1_9

## The first section deals with defining characteristic representations, introducing highest weight modules, Weyl modules, and building up to the Lusztig conjecture, with a diversion into Ext1 between simple modules for the algebraic group and the finite group.

Representations of Groups of Lie Type

10.1080/00927872.2018.1530249

## We also describe complete resolutions of the simple module over groups algebras of elementary abelian groups and quantum complete intersections.

On tensor products of complete resolutions

10.15446/recolma.v53nsupl.84006

## EnglishThe paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras.

Graded modules over simple Lie algebras

10.1016/j.jalgebra.2019.06.010

## We give, along the way, various characterizations of minimax modules, as well as a structural description of meager modules, which are defined as those that do not have the square of a simple module as subquotient.

Counting submodules of a module over a noetherian commutative ring

## We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.

The algebra of Boolean matrices, correspondence functors, and simplicity.

10.1142/S0219498821400156

## We prove the Kac-Wakimoto conjecture for the periplectic Lie superalgebra $\mathfrak{p}(n)$, stating that any simple module lying in a block of non-maximal atypicality has superdimension zero.

Kac-Wakimoto conjecture for the periplectic Lie superalgebra

10.1016/j.jalgebra.2020.02.036

## We give new improved bounds for the dominant dimension of Nakayama algebras and use those bounds to give a classification of Nakayama algebras with $n$ simple modules that are higher Auslander algebras with global dimension at least $n$.

On the classification of higher Auslander algebras for Nakayama algebras

10.1016/j.jalgebra.2020.04.027

## In this paper, we investigate the block that has an abelian defect group of rank $2$ and its Brauer correspondent has only one simple module.

Blocks with abelian defect groups of rank 2 and one simple module

10.4310/MRL.2019.V26.N2.A5

## We study the problem of indecomposability of translations of simple modules in the principal block of BGG category O for sl(n), as conjectured in [KiM1].

Indecomposable manipulations with simple modules in category $\mathcal{O}$

10.1007/S41980-018-0161-3

## if and only if $${\text {Hom}}(M/Z(M), S) \ne 0$$Hom(M/Z(M),S)≠0 for each singular simple module S.

On the Structure of Modules Defined by Opposites of FP Injectivity

10.1016/j.optcom.2018.09.008

## The notion of (semi)bricks, regarded as a generalization of (semi)simple modules, appeared in a paper of Ringel in 1976.

Gluing support {\tau}-tilting modules over {\tau}-tilting finite algebras

10.1016/j.aim.2020.107172

## Thus, once a formula for the characters of the indecomposable tilting $G$-modules has been found, a formula for the simple modules has been also.

On character formulas for simple and tilting modules.

10.5772/INTECHOPEN.82309

## Assume A is a basic connected and triangular algebra with n pairwise non-isomorphic simple modules.

Cyclotomic and Littlewood Polynomials Associated to Algebras

10.1515/jgth-2019-0130

## This generalises a result by Navarro for simple modules over finite p-solvable groups, which is the main motivation for this note.

A note on vertices of indecomposable tensor products

## Furthermore, using these concepts, we characterize some classical modules such as simple modules, S -Noetherian modules, and torsion-free modules.

On S-prime submodules

10.20527/EPSILON.V12I2.314

## Suppose that 𝑉𝑉[𝑝𝑝] is a class of Chen simple module for the Leavitt path algebra (𝐿𝐿𝐾𝐾 (𝐸𝐸)), with [p] being equivalent classes containing an infinite path.

SIFAT KEPRIMAAN MODUL SEDERHANA CHEN UNTUK GRAF

10.2140/ant.2020.14.1613

## We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy.

Classification of some vertex operator algebras of rank 3

## The simple objects of these categories are tensor modules as in the previously studied category, however, the choice of k provides more flexibility of nonsimple modules.

Integrable sl ( ∞ ) -modules and category O for gl ( m | n )

10.2140/INVOLVE.2019.12.919

## In this talk, we will introduce a class of truncated path algebras in which the Betti numbers of a simple module satisfy a polynomial of arbitrarily large degree.

Truncated path algebras and Betti numbers of polynomial growth

10.2140/involve.2019.12.1369

## A complete description of simple modules over $R$ is obtained by using the results of Irving and Gerritzen.

Nonsplit module extensions over the one-sided inverse of k[x]

10.1109/ICRA.2019.8793663

## Previous work on dynamic robot morphology has focused on simulation, combining simple modules, or switching between locomotion modes.

Self-Modifying Morphology Experiments with DyRET: Dynamic Robot for Embodied Testing

10.1016/J.IJDRR.2018.09.007

## The approach is based on a combination of three simple modules: 1) flood frequency analysis (frequency and peak discharge), 2) estimation of inundation depth, and 3) damage and loss estimation.

Flood risk mapping for direct damage to residential buildings in Quebec, Canada

10.1080/00927872.2019.1570233

## We describe the formal characters of some Weyl modules for simply connected and semisimple algebraic groups of type Dl over an algebraically closed field of characteristic where h is the Coxeter number, in the terms of the formal characters of simple modules.

Submodule structure of some Weyl modules and the cohomology for

10.1080/00927872.2018.1477951

## In previous work by the author, a class of finite-dimensional semisimple Hopf algebras was considered with respect to the question under what condition all but one isomorphism class of simple modules are one-dimensional.

On matched pairs defining Hopf algebras in a certain class

10.1007/s00209-020-02496-7

## We explain how this induces an isomorphism between the monoid of dominant monomials, used to parameterize simple modules, and a quotient of the monoid of rectangular semistandard Young tableaux.

Quantum affine algebras and Grassmannians.

## We investigate integral forms of certain simple modules over group algebras in characteristic 0 whose $p$-modular reductions have precisely three composition factors.

ON LATTICES OF INTEGRAL GROUP ALGEBRAS AND SOLOMON ZETA FUNCTIONS

## We add a simple module on the recently proposed hybrid semi-Markov CRF architecture and observe some promising results.

Towards Improving Neural Named Entity Recognition with Gazetteers

10.1142/S0219498819501883

## The commutative rings whose simple modules are indigent or injective are fully determined.

On the structure of modules defined by subinjectivity

10.1016/j.jpaa.2020.106529

## Furthermore, these simple modules when restricted as modules over N = 1 superconformal algebras coincide with those modules constructed in Yang et al.

On non-weight representations of the N = 2 superconformal algebras

10.1007/JHEP02(2020)004

## We establish the prescription for refined characters in higher rank minimal models from the dual $(A_{n-1},A_{m-1})$ theories in the large $m$ limit, and then provide evidence for Song's proposal to hold (at least) in some simple modules (including the vacuum module) at finite $m$.

Testing Macdonald Index as a Refined Character of Chiral Algebra

10.1016/J.AIM.2018.11.027

## We obtain a large family of simple modules that have a basis consisting of Gelfand–Tsetlin tableaux, the action of the Lie algebra is given by the Gelfand–Tsetlin formulas and with all Gelfand–Tsetlin multiplicities equal 1.

Combinatorial construction of Gelfand–Tsetlin modules for gln

10.1016/J.IJEPES.2019.03.054

## The proposed CHB2 inverter incorporates individual PV elements into modules that can dynamically connect to their neighbors not only in series but also in parallel, which reduces conduction losses and enables simple module balancing.

Concept of a distributed photovoltaic multilevel inverter with cascaded double H-bridge topology

10.1007/S40304-019-00180-9

## As a result, simple modules for the Schrödinger algebra which are locally finite over the positive part are completely classified.

Simple Singular Whittaker Modules Over the Schrödinger Algebra

10.1007/s11464-020-0846-9

## For all generic q ∈ ℂ*, when $$\mathfrak{g}$$ g is not of type A 1 , we prove that the quantum toroidal algebra $$U_q(\mathfrak{g}_{\rm{tor}})$$ U q ( g t o r ) has no nontrivial finite dimensional simple module.

Finite dimensional modules over quantum toroidal algebras

10.1007/s40863-019-00125-8

## The finite-dimensional simple modules over H and K, are classified; they all have dimension 1, respectively $$\le 2$$≤2.

On the bosonization of the super Jordan plane

10.1007/s00220-020-03882-2

## Vertex operator algebras are especially well suited for studying logarithmic conformal field theory (in which correlation functions have logarithmic singularities arising from non-semisimple modules for the chiral algebra) because of the logarithmic tensor category theory of Huang, Lepowsky, and Zhang.

Twisted modules and $G$-equivariantization in logarithmic conformal field theory.

10.1090/CONM/727/14633

## We establish a version of Ringel duality for this type of Lie superalgebras which allows to express the characters of tilting modules in terms of those of simple modules in that category.

Tilting modules for classical Lie superalgebras.

10.1080/00927872.2018.1530253

## We study the properties that these R-matrices have with respect to simple modules with the hope that this is a first step towards determining the existence of a (quantum) cluster algebra structure on a natural quotient of , the -algebra defined by Enomoto and Kashiwara, which the VV algebras categorify.

Convolution products and R-matrices for type B quiver Hecke algebras

10.1080/00927872.2019.1576184

Prime virtually semisimple modules and rings

10.1142/s0219498820502023

## At the end, we study abelian endoregular modules as subdirect products of simple modules.

Abelian Endoregular Modules

10.12988/ija.2019.915

## The main result shows that there are five d-dimensional simple modules over Poisson algebra A for any d ≥ 1.

Simple Poisson modules over certain polynomial Poisson algebras

10.1016/B978-0-444-64163-2.00002-5

## System behaviors generated by these simple modules include (1) linear growth and decline, (2) exponential growth and decline, (3) logistic growth, (4) overgrowth and collapse, (5) oscillations, and (6) time lags.

Basic building blocks of system structure and behavior