H_T Vertex Algebras

2006/02/28 by Maarten J Bergvelt, Bergvelt, Maarten J
Mathematics · Physics and Astronomy · #17B69 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:17B69

paper · pdf · doi:10.48550/arxiv.math/0602671

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

arxiv created 2006/02/28 · arxiv updated 2009/12/01

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.

Related

• H_T Vertex Algebras and the Infinite Toda Lattice
• H_D-Quantum Vertex Algebras and Bicharacters
• A unified construction of vertex algebras from infinite-dimensional Lie algebras
• Vertex algebras generated by Lie algebras
• Vertex operators and the class algebras of symmetric groups