Jet modules for the centerless Virasoro-like algebra
Abstract
In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a $2$-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over $\mathfrak{sl}_2$. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of \cite{BB, BZ}. Consequently, indecomposable jet modules are described using modules over the algebra $\BB_+$, which is the "positive part" of a Block type algebra studied first by \cite{DZ} and recently by \cite{IM, I}).
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.02034
- arXiv:
- arXiv:1611.02034
- Bibcode:
- 2016arXiv161102034G
- Keywords:
-
- Mathematics - Representation Theory;
- 17B10;
- 17B20;
- 17B65;
- 17B66;
- 17B68
- E-Print:
- 21 pages