Chinese Quarterly Journal of Mathematics ›› 2020, Vol. 35 ›› Issue (2): 194-198.doi: 10.13371/j.cnki.chin.q.j.m.2020.02.007

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

  

  1. School of Mathematics and statistics, Henan University, Kaifeng 475004, China
  • Received:2019-12-09 Online:2020-06-30 Published:2020-09-03
  • Contact: NIU Meng-nan(1995-), male, native of Jincheng, Shanxi, a postgraduate of Henan University, engages in representation theory of Lie algebras.
  • About author:NIU Meng-nan(1995-), male, native of Jincheng, Shanxi, a postgraduate of Henan University, engages in representation theory of Lie algebras.

Abstract: In this paper, we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of in nite 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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