The radical of a vertex operator algebra
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The radical $J(V)$ of a vertex operator algebra $V$ is defined to be the subspace of $V$ consisting of vectors $v$ such that the zero mode $o(v)=0$ on $V$ where $o(v)=v_{wt v-1}$ if $v$ is homogeneous. We establish various facts about $o(v),$ including the determination of $J(V)$ which is shown to be essentially equal to $(L(0)+L(-1))V.$
tex 10 pages, to appear in : Proc. of the Conference on the Monster and Lie algebras at The Ohio State University, May 1996
tex 10 pages, to appear in : Proc. of the Conference on the Monster and Lie algebras at The Ohio State University, May 1996