Modules over the algebra Vir(a, b)

作者：Han, Jianzhi; Chen, Qiufan^*; Su, Yucai

来源：Linear Algebra and Its Applications, 2017, 515: 11-23.

DOI：10.1016/j.laa.2016.11.002

• The algebra Vir(a, b)
• The algebra W(a, b)
• Non-weight modules
• Central extensions

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) not equal (0,1), where W(a, b) is the Lie algebra with basis {L-n, W-n | n is an element of Zeta} and relations [L-m, L-n] = (n-m)Lm+n , [L-m, W-n] = (a+n+b(m))Wm+n, [W-m, 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 circle plus CW0)-modules of rank 1. It is proved that such modules can only exist for a is an element of Z.

• 出版日期2017-2-15
• 单位同济大学; 上海海事大学