A smash product construction of nonlocal vertex algebras

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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 languageEnglish (US)
Pages (from-to)605-637
Number of pages33
JournalCommunications in Contemporary Mathematics
Volume9
Issue number5
DOIs
StatePublished - Oct 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

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

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