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Related papers: Loop super-Virasoro Lie conformal superalgebra

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In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

Representation Theory · Mathematics 2025-01-06 Lipeng Luo , Yucai Su , Mengjun Wang

We first define a class of non-weight modules over the N=1 Heisenberg-Virasoro superalgebra $\mathfrak{g}$, which are reducible modules. Then we give all submodules of such modules, and present the corresponding irreducible quotient modules…

Representation Theory · Mathematics 2025-08-13 Ziqi Hong , Haibo Chen , Yucai Su

The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be…

Representation Theory · Mathematics 2013-01-04 Xiangqian Guo , Rencai Lu , Kaiming Zhao

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

Representation Theory · Mathematics 2020-05-13 Chunguang Xia

Let $\delta=0$ or $\frac{1}{2}$. In this paper, we introduce the Fermion algebra $F(\delta)$ and the Fermion-Virasoro algebra $\mathcal S(\delta)$. They are infinite-dimensional Lie superalgebras. All simple smooth $F(\delta)$-modules, all…

Representation Theory · Mathematics 2023-06-28 Yaohui Xue , Kaiming Zhao

Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible…

Representation Theory · Mathematics 2019-07-05 Lipeng Luo , Yanyong Hong , Zhixiang Wu

A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…

Mathematical Physics · Physics 2015-06-11 A. Babichenko , D. Ridout

In this paper, we introduce a class of infinite Lie conformal algebras $\mathfrak{B}(\alpha,\beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $\mathfrak{B}(p)$ and its non-trivial conformal modules of $\Z$-graded…

Representation Theory · Mathematics 2020-07-21 Haibo Chen , Yanyong Hong , Yucai Su

In this paper, we construct a family of non-weight modules over the super-Virasoro algebras. Those modules when regarded as modules of the Ramond algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{h}$ are free…

Representation Theory · Mathematics 2020-07-09 Hengyun Yang , Yufeng Yao , Limeng Xia

For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $\sigma$ that commutes with $d$, we introduce the $(d,\sigma)$-twisted Affine-Virasoro…

Representation Theory · Mathematics 2025-07-02 Rencai Lü , Xizhou You , Kaiming Zhao

In this paper, we classify the following simple $\mathbb{Z}$-graded Lie conformal algebras $\mathcal{L}=\bigoplus_{i\in \mathbb{Z}}\mathcal{L}_i$ such that (1)$rank\mathcal{L}_i\leq 1$, (2)$\mathcal{L}_0$ is the Virasoro Lie conformal…

Rings and Algebras · Mathematics 2025-03-12 Maosen Xu

Let $HV$ be the loop Heisenberg-Virasoro Lie algebra over $\C$ with basis $\{L_{\a,i},H_{\b,j}\,|\,\a,\,\b,i,j\in\Z\}$ and brackets $[L_{\a,i},L_{\b,j}]=(\a-\b)L_{\a+\b,i+j}, [L_{\a,i},H_{\b,j}]=-\b H_{\a+\b,i+j},[H_{\a,i},H_{\b,j}]=0$. In…

Rings and Algebras · Mathematics 2015-06-22 Guangzhe Fan , Yucai Su , Henan Wu

In this paper, we study conformal biderivations of a Lie conformal algebra. First, we give the definition of conformal biderivation. Next, we determine the conformal biderivations of loop $W(a,b)$ Lie conformal algebra, loop Virasoro Lie…

Rings and Algebras · Mathematics 2019-04-10 Jun Zhao , Liangyun Chen , Lamei Yuan

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

The notion of a Lie conformal superalgebra encodes an axiomatic descrption of singular parts of the operator product expansions of chiral fields in conformal field theory. In the paper we give a detailed proof of the classification of all…

Mathematical Physics · Physics 2014-01-17 Davide Fattori , Victor G. Kac

We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.

Representation Theory · Mathematics 2019-07-12 Rekha Biswal , Abdelkarim Chakhar , Xiao He

We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give…

Representation Theory · Mathematics 2020-07-07 Yan-an Cai , Rencai Lü , Yan Wang

This paper is devoted to investigating the structure theory of a class of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we completely determine the derivation algebras, the automorphism…

Rings and Algebras · Mathematics 2016-07-19 Juanjuan Li , Guangzhe Fan

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

We study irreducible modules for map Heisenberg-Virasoro algebras. In particular, we give a complete classification of irreducible Harish-Chandra modules for map Heisenberg-Virasoro algebras. We will also classify non-weight irreducible…

Representation Theory · Mathematics 2023-11-07 Priyanshu Chakraborty