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 |
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| container_title | Linear algebra and its applications |
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| creator | Han, Jianzhi Chen, Qiufan Su, Yucai |
| description | 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. |
| doi_str_mv | 10.1016/j.laa.2016.11.002 |
| format | Article |
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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. 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| subjects | Algebra Central extensions Complex numbers Complexity theory Integer programming Lie groups Linear algebra Modules Non-weight modules The algebra [formula omitted] Weight |
| title | Modules over the algebra Vir(a,b) |
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