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<p>Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu–Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra. In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra. As an application we obtain all simple weak <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3733_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-twisted modules over some vertex operator superalgebras.</p>

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Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras

  • 期刊论文

  • 发表日期：

    2025年4月11日

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  • Yulu Chen,
  • Yufeng Yao,
  • Kaiming Zhao

摘要

Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu–Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra. In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra. As an application we obtain all simple weak \(\psi \) ψ -twisted modules over some vertex operator superalgebras.