Finite irreducible modules of a class of ℤ⁺-graded Lie conformal algebras

2021/05/28 by Maosen Xu, Yanyong Hong, Xu, Maosen +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2105.13657

openalex publication_date 2021/05/28 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of ℤ⁺-graded Lie conformal algebras L=\bigoplus_i=0^∞ ℂ[∂]L_i satisfying [L_0λL₀]=(∂+2λ)L₀, and [L_1λL_i]≠ 0 for any i∈ ℤ⁺. These Lie conformal algebras include Block type Lie conformal algebra B(p) and map Virasoro Lie conformal algebra V(ℂ[T])=Vir⊗ ℂ[T]. As a result, we show that all non-trivial finite irreducible modules of these algebras are free of rank one as a ℂ[∂]-module.

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