Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies
Gribanov, V. V. ; Kadyshevsky, V. G. ; Sorin, A. S.
arXiv, 0505039 / Harvested from arXiv
Text on arXiv
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as particular cases. We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators with involution generalizing the graded commutator in superalgebras, which allows one to describe these hierarchies in the framework of the Hamiltonian formalism and construct their first two Hamiltonian structures. The first Hamiltonian structure is obtained for both bosonic and fermionic Lax operators while the second Hamiltonian structure is established for bosonic Lax operators only.
Publié le : 2005-05-14
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  High Energy Physics - Theory,  Mathematical Physics 
@article{0505039,
     author = {Gribanov, V. V. and Kadyshevsky, V. G. and Sorin, A. S.},
     title = {Hamiltonian structures of fermionic two-dimensional Toda lattice
  hierarchies},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505039}
}

Gribanov, V. V.; Kadyshevsky, V. G.; Sorin, A. S. Hamiltonian structures of fermionic two-dimensional Toda lattice
  hierarchies. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505039/