H_T Vertex Algebras

Details H_T Vertex Algebras H_T Vertex Algebras

2006-02-28

arxiv.org/abs/math/0602671v1

Mathematics

Quantum Algebra

Contribution to the Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications" in honor of

Scientific paper

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.

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