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H_T Vertex Algebras

Maarten J Bergvelt
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Abstract

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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Maarten J Bergvelt. 2006-02-28. H_T Vertex Algebras. https://arxiv.org/abs/math/0602671

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