H_T Vertex Algebras
Abstract
Description
The usual vertex algebras have as underlying symmetry the Hopf algebra $H_D=\mathbb C[D]$ of infinitesimal translations. We show that it is possible to replace $H_D$ by another symmetry algebra $H_T=\mathbb C[T,T\inv]$, the group algebra of the Abelian group generated by $T$. $H_T$ is the algebra of symmetries of a lattice of rank 1, and the construction gives a class of vertex algebras related to the Infinite Toda Lattice in the same way as the usual $H_D$-vertex algebras are related to Korteweg-de Vries hierarchies.
Contribution to the Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications" in honor of Jim Lepowsky and Robert Wilson
Contribution to the Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications" in honor of Jim Lepowsky and Robert Wilson