A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra

We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA V-Lambda. We show that a generalized deep hole defines a 'true' automorphism invariant deep hole of the Leech lattice. We also show that there is a correspondence between the set of isomorphism classes of holomorphic VOA V of central charge 24 having non-abelian V1 and the set of equivalence classes of pairs (tau,beta) satisfying certain conditions, where tau is an element of Co.0 and beta is a tau-invariant deep hole of squared length 2. It provides a new combinatorial approach towards the classification of holomorphic VOAs of central charge 24. In particular, we give an explanation for an observation of G. H & ouml;hn, which relates the weight one Lie algebras of holomorphic VOAs of central charge 24 to certain codewords associated with the glue codes of Niemeier lattices.