Modules over the algebra Vir(a,b)

Modules over the algebra Vir(a,b)

For any two complex numbers a and b, Vir(a,b) is a central extension of W(a,b) which is universal in the case (a,b)≠(0,1), where W(a,b) is the Lie algebra with basis {Ln,Wn|n∈Z} and relations [Lm,Ln]=(n−m)Lm+n, [Lm,Wn]=(a+n+bm)Wm+n, [Wm,Wn]=0. In this paper, we construct and classify a class of non-...

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Veröffentlicht in:Linear algebra and its applications 2017-02, Vol.515, p.11-23
Hauptverfasser: Han, Jianzhi, Chen, Qiufan, Su, Yucai
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Central extensions
Complex numbers
Complexity theory
Integer programming
Lie groups
Linear algebra
Modules
Non-weight modules
The algebra [formula omitted]
Weight
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Zusammenfassung:For any two complex numbers a and b, Vir(a,b) is a central extension of W(a,b) which is universal in the case (a,b)≠(0,1), where W(a,b) is the Lie algebra with basis {Ln,Wn|n∈Z} and relations [Lm,Ln]=(n−m)Lm+n, [Lm,Wn]=(a+n+bm)Wm+n, [Wm,Wn]=0. In this paper, we construct and classify a class of non-weight modules over the algebra Vir(a,b) which are free U(CL0⊕CW0)-modules of rank 1. It is proved that such modules can only exist for a∈Z.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.11.002