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In this paper, we give a complete classification of irreducible bounded weight modules over the derivation Lie algebras of rational quantum tori

Representation Theory · Mathematics 2020-01-10 Genqiang Liu , Kaiming Zhao

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

Representation Theory · Mathematics 2008-02-23 Dijana Jakelic , Adriano Moura

We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such…

Representation Theory · Mathematics 2012-08-24 Viktor Bekkert , Georgia Benkart , Vyacheslav Futorny , Iryna Kashuba

In this paper, the conjugate-linear anti-involutions and the unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified respectively. We prove that any unitary irreducible module of…

Rings and Algebras · Mathematics 2012-01-09 Xiufu Zhang , Shaobin Tan

The category of level zero representations of current and affine Lie algebras shares many of the properties of other well-known categories which appear in Lie theory and in algebraic groups in characteristic p and in this paper we explore…

Representation Theory · Mathematics 2015-04-14 Matthew Bennett , Vyjayanthi Chari

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal…

Representation Theory · Mathematics 2025-05-22 Chengkang Xu , Fulin Chen , Shaobin Tan

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 we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extension of G tensor A where G is a basic classical Lie superalgebra and A is a Laurent polynomial ring in…

Representation Theory · Mathematics 2012-05-17 S. Eswara Rao

Let $n>1$ be an integer, $\alpha\in{\mathbb C}^n$, $b\in{\mathbb C}$, and $V$ a $\mathfrak{gl}_n$-module. We define a class of weight modules $F^\alpha_{b}(V)$ over $\sl_{n+1}$ using the restriction of modules of tensor fields over the Lie…

Representation Theory · Mathematics 2019-08-08 Vyacheslav Futorny , Genqiang Liu , Rencai Lu , Kaiming Zhao

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.

Representation Theory · Mathematics 2016-06-17 Ibrahim Assem , Ralf Schiffler , Khrystyna Serhiyenko

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

Quantum Algebra · Mathematics 2007-05-23 Stephen Berman , Chongying Dong , Shaobin Tan

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\tau$. More specifically, we define and study two categories $\mathcal{E}_{\tau}$ and $\mathcal{C}_{\tau}$ of…

Representation Theory · Mathematics 2013-09-09 Hongyan Guo , Shaobin Tan , Qing wang

In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…

Mathematical Physics · Physics 2007-05-23 Victor G. Kac

Let L be a finite-dimensional Lie algebra over a field of non-zero characteristic. By a theorem of Jacobson, L has a finite-dimensional faithful module which is completely reducible. We show that if the field is not algebraically closed,…

Representation Theory · Mathematics 2019-02-13 Donald W. Barnes

In this paper, we first construct the twisted full toroidal Lie algebra by an extension of a centreless Lie torus $LT$ which is a multiloop algebra twisted by several automorphisms of finite order and equipped with a particular grading. We…

Representation Theory · Mathematics 2021-03-22 Souvik Pal , S. Eswara Rao

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion…

Quantum Algebra · Mathematics 2012-12-20 Bojko Bakalov , Alessandro D'Andrea , Victor G. Kac

We introduce a new class of extended affine Lie algebras called Hamiltonian Extended Lie Algebras(HEALAs). They are so called because the corresponding derivation algebra is the classical Hamiltonian algebra. We classify the irreducible…

Representation Theory · Mathematics 2022-03-01 S Eswara Rao

We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…

High Energy Physics - Theory · Physics 2008-02-03 S. Krivonos , A. Sorin

We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a…

Representation Theory · Mathematics 2007-05-23 Alice Fialowski , Michael Penkava

Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine superalgebras…

Representation Theory · Mathematics 2014-04-03 Yuezhu Wu , R. B. Zhang