Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-10 DOI:10.1142/s0219199724500214

Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao

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Abstract

In this paper, we present a determinant formula for a contravariant form on Verma modules over the $N = 1$ Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the $N = 1$ BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the $N = 1$ BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the $N = 1$ BMS superalgebra, which includes Fock modules and certain Whittaker modules.

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N = 1 邦迪-梅兹纳-萨克斯超代数上的光滑模块

在本文中，我们提出了关于 N=1 邦迪-梅兹纳-萨克斯（BMS）超代数上的维尔马模块的协变形式的行列式。该公式为 Verma 模块的不可还原性建立了必要条件和充分条件。然后，我们引入并描述了一类简单光滑模块，它们概括了 N=1 BMS 上代数的 Verma 模块和 Whittaker 模块。我们还利用海森堡-克利福德顶点超代数构建了 N=1 BMS 超代数的自由场实现。通过这个自由场实现，我们可以得到 N=1 BMS 上代数的自然光滑模块族，其中包括福克模块和某些惠特克模块。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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