The regular representations and the \(A_n(V)\)-algebras (Q2782391)

A family of generalized Zhu's algebras \(A_n(V)\) were introduced for a vertex operator algebra \(V\) by \textit{C. Dong, H. Li} and \textit{G. Mason} [J. Algebra 206, 67-96 (1998; Zbl 0911.17017)]. In his earlier work [J. Algebra 238, 159-193 (2001; Zbl 1060.17015)], the author introduced weak \(V\otimes V\)-modules \({\mathcal D}_{P(z)} (V,U)\) for any vector space \(U\) and a complex number \(z\). In this paper, he relates \(A_n(V)\)-theory to the (generalized) regular representations of \(V\) on \({\mathcal D}_{P(-1)} (V,U)\).NEWLINENEWLINEFor the entire collection see [Zbl 0980.00029].