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

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=⨁i=0∞C[∂]Li satisfying [L0λL0]=(∂+2λ)L0, and [L1λLi]≠0 for any i∈Z+. These Lie conformal alg...

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Published in:Journal of pure and applied algebra 2023-08, Vol.227 (8), p.107351, Article 107351
Main Authors: Xu, Maosen, Hong, Yanyong
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Language:English
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[formula omitted]-graded Lie conformal algebra
Block type Lie conformal algebra
Finite irreducible module
Map Virasoro conformal algebra
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description 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=⨁i=0∞C[∂]Li satisfying [L0λL0]=(∂+2λ)L0, and [L1λLi]≠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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subjects [formula omitted]-graded Lie conformal algebra
Block type Lie conformal algebra
Finite irreducible module
Map Virasoro conformal algebra
title Finite irreducible modules of a class of Z+-graded Lie conformal algebras
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