Collision Index and Stability of Elliptic Relative Equilibria in Planar {n}-body Problem

In this article, we construct three new holomorphic vertex operator algebras of central charge 24 using the \({\mathbb{Z}_{2}}\)-orbifold construction associated to inner automorphisms. Their weight one subspaces have the Lie algebra structures D_7,3A_3,1G_2,1, E_7,3A_5,1, and \({A_{8,3}A_{2,1}^2}\). In addition, we discuss the constructions of holomorphic vertex operator algebras with Lie algebras A_5,6C_2,3A_1,2 and \({D_{6,5}A_{1,1}^2}\) from holomorphic vertex operator algebras with Lie algebras C_5,3G_2,2A_1,1 and \({A_{4,5}^2}\), respectively.