RESEARCH ARTICLE

Irreducible A(1)1 -modules from modules over two-dimensional non-abelian Lie algebra

  • Genqiang LIU ,
  • Yueqiang ZHAO
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  • School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

Received date: 13 Apr 2015

Accepted date: 05 Oct 2015

Published date: 18 Apr 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

For any module V over the two-dimensional non-abelian Lie algebra b and scalar α∈ℂ, we define a class of weight modules Fα(V) with zero central charge over the affine Lie algebra A(1)1. These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα(V) to be irreducible. In this way, we obtain a lot of irreducible weight A(1)1-modules with infinite-dimensional weight spaces.

Cite this article

Genqiang LIU , Yueqiang ZHAO . Irreducible A(1)1 -modules from modules over two-dimensional non-abelian Lie algebra[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 353 -363 . DOI: 10.1007/s11464-016-0503-5

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