Restricted modules for gap-p Virasoro algebra and twisted modules for certain vertex algebras

2022/02/27 by Guo Hongyan, Guo, Hongyan, Chengkang Xu +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2202.13342

openalex publication_date 2022/02/27 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

This paper studies restricted modules of gap-p Virasoro algebra Ł and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted Ł-modules of level \el and the category of twisted modules of vertex algebra V_N_p(\el,0), where N_p is a new Lie algebra, \el:=(ℓ₀,0,⋯,0)∈\C^\halfp+1, ℓ₀∈\C is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted Ł-modules of level \el. More explicitly, we give a uniform construction of simple restricted Ł-modules as induced modules. We present several equivalent characterizations of simple restricted Ł-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of Ł. Moreover, simple restricted Ł-modules of level \el are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted Ł-modules of level \el (including Whittaker modules).

Related

• q-Virasoro algebra and vertex algebras
• Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra
• The restriction of polynomial modules for the Virasoro algebra to \mathfraksl₂ ( \cc )
• Simple restricted modules over the Heisenberg-Virasoro algebra as VOA modules
• Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra