Simple Bounded Weight Modules for the Vector Field Lie Algebras of Infinite Rank

NIU Meng-nan

doi:10.13371/j.cnki.chin.q.j.m.2020.02.007

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 2: 194 - 198

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.02.007

Simple Bounded Weight Modules for the Vector Field Lie Algebras of Infinite Rank

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School of Mathematics and statistics, Henan University, Kaifeng 475004, China

NIU Meng-nan(1995-), male, native of Jincheng, Shanxi, a postgraduate of Henan University, engages in representation theory of Lie algebras.

Received date: 2019-12-09

Online published: 2020-09-03

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Abstract

In this paper, we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of innite rank. It turns out that any such modules are intermediate series modules. This result is very different from the vector eld Lie algebra Wd of nite rank.

Key words： Vector eld Lie algebra; Weight module; Intermediate series module

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NIU Meng-nan . Simple Bounded Weight Modules for the Vector Field Lie Algebras of Infinite Rank[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(2) : 194 -198 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.007

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