Boundary Lax pairs from non-ultra local Poisson algebras

Jean Avan, Anastasia Doikou

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We consider non-ultra local linear Poisson algebras on a continuous line . Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or "boundary" extensions. They are parametrized by a "boundary" scalar matrix and depend in addition on the choice of an anti-automorphism. The new algebras are the classical-linear counterparts of known quadratic quantum boundary algebras. For any choice of parameters the non-ultra local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary PCM model is examined as a physical example.
Original languageEnglish
Article number113512
JournalJournal of Mathematical Physics
Issue number11
Publication statusPublished - Nov 2009


  • math-ph
  • hep-th
  • math.MP
  • nlin.SI


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