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We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…

Representation Theory · Mathematics 2021-05-17 Lucas Calixto , Tiago Macedo

In this paper, we define the induced modules of Lie algebra ad$(B)$ associated with a 3-Lie algebra $B$-module, and study the relation between 3-Lie algebra $A_{\omega}^{\delta}$-modules and induced modules of inner derivation algebra…

Rings and Algebras · Mathematics 2019-07-02 Ruipu Bai , Yue Ma , Pei Liu

Given a finite-dimensional module, $V$, for a finite-dimensional, complex, semi-simple Lie algebra $\lie g$ and a positive integer $m$, we construct a family of graded modules for the current algebra $\lie g[t]$ indexed by simple $\CC\lie…

Representation Theory · Mathematics 2015-09-11 Matthew Bennett , Rollo Jenkins

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

Rings and Algebras · Mathematics 2013-01-10 Ievgen Makedonskyi , Anatoliy Petravchuk

Let $\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g},…

Representation Theory · Mathematics 2021-05-18 Lucas Calixto , Tiago Macedo

For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…

Rings and Algebras · Mathematics 2013-01-22 Donald W. Barnes

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

Mathematical Physics · Physics 2010-05-12 Carina Boyallian , Victor G. Kac , Jose I. Liberati , Alexei Rudakov

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…

Representation Theory · Mathematics 2009-06-11 Sofiane Bouarroudj , Pavel Grozman , Dimitry Leites

Toroidal Lie algebras are universal central extentions of the finite dimensional simple Lie algbera tensored with Laurent Polynomials in several commuteing variables. In this paper we classify irreducible integrable modules for Toroidal Lie…

Representation Theory · Mathematics 2007-05-23 S. Eswara Rao

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…

Rings and Algebras · Mathematics 2007-05-23 L. A. Simonian

We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…

Rings and Algebras · Mathematics 2016-08-17 E. N. Marcos , O. Mendoza , C. Sáenz , V. Santiago

In this paper, we study a class of infinite simple Lie conformal algebras associated to a class of generalized Block type Lie algebras. The central extensions, conformal derivations and free intermediate series modules of this class of Lie…

Representation Theory · Mathematics 2019-07-01 Yanyong Hong , Yang Pan , Haibo Chen

We find a new representation of the simple Lie algebra of type $E_6$ on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and…

Representation Theory · Mathematics 2011-12-19 Xiaoping Xu

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

Representation Theory · Mathematics 2026-04-13 Siddhartha Sahi , Hadi Salmasian , Vera Serganova

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…

Representation Theory · Mathematics 2018-04-09 Vyacheslav Futorny , Iryna Kashuba

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

Quantum Algebra · Mathematics 2012-06-19 Hebing Rui

In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the…

Rings and Algebras · Mathematics 2011-03-10 Georgia Benkart , Alberto Elduque

We prove that the tensor product of a simple and a finite dimensional $\mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $\mathfrak{q}(n)$-supermodules to that of simple…

Representation Theory · Mathematics 2018-07-12 Chih-Whi Chen , Kevin Coulembier , Volodymyr Mazorchuk

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated…

Quantum Algebra · Mathematics 2013-12-18 Kenichiro Tanabe

This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…

Representation Theory · Mathematics 2025-09-03 Volodymyr Mazorchuk , Xiaoyu Zhu