SEMINARS
Modules over the algebra $Vir(a, b)$

2017-04-21　10:30 — 11:30

Middle Lecture Room

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 $(a,b)\ne(0,1)$, where $W(a,b)$ is the
Lie algebra with basis $\{L_n, W_n | n \in {\mathbb Z}\}$ and relations
$[L_m, L_n]=(n−m)L_{m+n}, [L_m, W_n]=(a+n+bm)W_{m+n}, [W_m,W_n]=0.$
In this talk, we present a class of non-weight modules over the algebra $Vir(a, b)$
which are free $U({\mathbb C}L_0\plus{\mathbb C}W_0)$-modules of rank $1$. It is
proved that such modules can only exist for $a\in Z$.