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

doi:10.1007/s11464-016-0503-5

Front. Math. China

2016, Vol. 11

Issue (2) : 353-363 https://doi.org/10.1007/s11464-016-0503-5

RESEARCH ARTICLE

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

Genqiang LIU(

),Yueqiang ZHAO

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

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Abstract

For any module V over the two-dimensional non-abelian Lie algebra b and scalar α∈?, we define a class of weight modules F^α(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 F^α(V) to be irreducible. In this way, we obtain a lot of irreducible weight A⁽¹⁾₁-modules with infinite-dimensional weight spaces.

Keywords Affine Lie algebras irreducible modules weight modules

Issue Date: 18 April 2016

Cite this article:

Genqiang LIU,Yueqiang ZHAO. Irreducible A⁽¹⁾₁ -modules from modules over two-dimensional non-abelian Lie algebra[J]. Front. Math. China, 2016, 11(2): 353-363.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0503-5
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I2/353

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