Simple Harish-Chandra modules over the superconformal current algebra

Fuente: arXiv
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Main Authors: He, Y., Liu, D., Wang, Y.
Format: Preprint
Published: 2025
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author He, Y.
Liu, D.
Wang, Y.
author_facet He, Y.
Liu, D.
Wang, Y.
contents In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g} \otimes \mathcal{A}\oplus \mathbb CC_1$, where $\dot{\frak g}$ is a finite-dimensional simple Lie algebra, and $\mathcal{A}$ is the tensor product of the Laurent polynomial algebra and the Grassmann algebra. As an application, we can directly get the classification of the simple Harish-Chandra modules over the $N=1$ Heisenberg-Virasoro algebra.
format Preprint
id arxiv_https___arxiv_org_abs_2502_19139
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Simple Harish-Chandra modules over the superconformal current algebra
He, Y.
Liu, D.
Wang, Y.
Representation Theory
In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g} \otimes \mathcal{A}\oplus \mathbb CC_1$, where $\dot{\frak g}$ is a finite-dimensional simple Lie algebra, and $\mathcal{A}$ is the tensor product of the Laurent polynomial algebra and the Grassmann algebra. As an application, we can directly get the classification of the simple Harish-Chandra modules over the $N=1$ Heisenberg-Virasoro algebra.
title Simple Harish-Chandra modules over the superconformal current algebra
topic Representation Theory
url https://arxiv.org/abs/2502.19139