The solenoidal Virasoro algebra and its simple weight modules.

AbstractThe aim of this paper is to construct a one dimensional universal central extension of the solenoidal Lie algebra W(n)μ introduced by Y. Billig and V. Futorny. The obtained Lie algebra is higher rank Virasoro algebra denoted by Vir(n)μ. Moreover, we study Vir(n)μ-Harich-Chandra modules. We obtain two kinds of Harich-Chandra modules, the intermediate series modules and generalized weight modules. Furthermore, we use the triangular decomposition of Vir(n)μ given by lexicographic order on Zn to construct new weight modules having infinite dimensional weight spaces. [ABSTRACT FROM AUTHOR]