%0 Journal Article
%T Quasi root systems and vertex operator realizations of the Virasoro algebra
%A Boris Noyvert
%J Mathematics
%D 2009
%I arXiv
%X A construction of the Virasoro algebra in terms of free massless two-dimensional boson fields is studied. The ansatz for the Virasoro field contains the most general unitary scaling dimension 2 expression built from vertex operators. The ansatz leads in a natural way to a concept of a quasi root system. This is a new notion generalizing the notion of a root system in the theory of Lie algebras. We introduce a definition of a quasi root system and provide an extensive list of examples. Explicit solutions of the ansatz are presented for a range of quasi root systems.
%U http://arxiv.org/abs/0912.0557v1