Imaginary Verma modules for the twisted affine Nappi-Witten Lie algebra \(\widetilde{H}_4[\sigma]\)
type: Item
instance of: scholarly article
title: Imaginary Verma modules for the twisted affine Nappi-Witten Lie algebra \(\widetilde{H}_4[\sigma]\)
zbMATH Open document ID: 1487.17015
author: Xue Chen
published in: Hokkaido Mathematical Journal
publication date: 2022-01-27T00:00:00Z
review text: The Nappi-Witten Lie algebra \(H_4\) is a four-dimensional Lie algebra over \(\mathbb{C}\) generated by \(a, b, c, d\) with the following Lie bracket \([a, b] = c, [d, a] = a, [d, b] = -b, [c, H_4] = 0.\) The affine Nappi-Witten Lie algebra is defined as \(\hat{H}_4=H_4\otimes\mathbb{C}[t, t^{-1}] \oplus \mathbb{C}K\) equipped with some Lie bracket. The twisted affine Nappi-Witten Lie algebra \(\hat{H}_4[\sigma]\) is a subalgebra of \(\hat{H}_4\). The direct sum of \(\hat{H}_4[\sigma]\) with \(\mathbb{C}D\) is denoted by \(\tilde{H}_4[\sigma]\), which is also called a twisted affine Nappi-Witten Lie algebra since \([K,D]=0,[D,x\otimes t^n]=nx\otimes t^n\). In this paper, the author gave an irreducible criterion for the imaginary Verma modules for the twisted affine Nappi-Witten Lie algebra \(\tilde{H}_4[\sigma]\). When the imaginary Verma module is reducible, the author determined the explicit characterizations of the maximal submodule, imaginary vacuum vectors, and the composition structure.
reviewed by: Zhanqiang Bai
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 7465474
zbMATH Keywords: imaginary vacuum vectors
zbMATH Keywords: imaginary Verma modules
zbMATH Keywords: twisted affine Nappi-Witten Lie algebra
Wikidata QID: Q115237665
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/2019-169
OpenAlex ID: W4200270372
cites work: Representations of affine Nappi-Witten algebras
cites work: Classification of irreducible non-zero level quasifinite modules over twisted affine Nappi-Witten algebra
cites work: Whittaker modules for the twisted affine Nappi-Witten Lie algebra \(\widehat{H}_4 [\tau]\)
cites work: String interactions in gravitational wave backgrounds
cites work: The abelian cosets of the Heisenberg group
cites work: Imaginary Verma Modules for Affine Lie Algebras
cites work: Extension of Vertex Operator Algebra $V_{\widehat{H}_{4}}(\ell,0)$
cites work: Q4040877
cites work: String propagation in gravitational wave backgrounds
cites work: Wess-Zumino-Witten model based on a nonsemisimple group
cites work: Non-Abelian bosonization in two dimensions
DOI: 10.14492/HOKMJ/2019-169
description: scientific article; zbMATH DE number 7465474