## Abstract

A notion of vertex bialgebra and a notion of nonlocal vertex module-algebra for a vertex bialgebra are studied and then a smash product construction of nonlocal vertex algebras is presented. For every nonlocal vertex algebra V satisfying a suitable condition, a canonical bialgebra S(V) is constructed such that primitive elements of B(V) are essentially pseudo-derivations and group-like elements are essentially pseudo-endomorphisms. As an application, vertex algebras associated with the Heisenberg Lie algebras as well as those associated with the nondegenerate even lattices are reconstructed through smash products, and furthermore, a different approach to the construction of modules for the lattice vertex algebras is given.

Original language | English (US) |
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Pages (from-to) | 605-637 |

Number of pages | 33 |

Journal | Communications in Contemporary Mathematics |

Volume | 9 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2007 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Keywords

- Pseudo-derivation
- Pseudoendomorphism
- Vertex bialgebra
- Vertex module-algebra