It is well known that Galilean conformal algebras play important roles in the nonrelativistic anti-de Sitter/conformal field theory correspondence. The finite Lie conformal algebras P G ( a , b ) of planar Galilean type can be viewed as Lie conformal analogues of certain planar Galilean conformal algebras. In this paper, we classify finite irreducible conformal modules over P G ( a , b ) for all complex numbers a and b.

中文翻译：

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平面伽利略型有限李保形代数的不可约表示

众所周知，伽利略共形代数在非相对论反德西特/共形场论对应中起着重要作用。平面伽利略类型的有限李保形代数 PG ( a , b ) 可以看作是某些平面伽利略保形代数的李保形类似物。在本文中，我们针对所有复数 a 和 b 对 PG ( a , b ) 上的有限不可约共形模进行分类。