A smash product construction of nonlocal vertex algebras

Abstract

A notion of vertex bialgebra and a notion of module nonlocal vertex 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 $B(V)$ is constructed such that primitive elements of $B(V)$ are essentially pseudo derivations and group-like elements are essentially pseudo endomorphisms. Furthermore, vertex algebras associated with Heisenberg Lie algebras as well as those associated with nondegenerate even lattices are reconstructed through smash products.

30 pages

References in corpus (2)

• Field Algebras
• Constructing quantum vertex algebras

Cited by in corpus (1)

• Vertex coalgebras, comodules, cocommutativity and coassociativity