Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies

Details Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies

2005-05-14

arxiv.org/abs/nlin/0505039v1

Theor.Math.Phys. 146 (2006) 73-84; Teor.Mat.Fiz. 146 (2006) 90-102

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTeX, the talks delivered at the International Workshop on Classical and Quantum Integrable Systems (Dubna, January

Scientific paper

10.1007/s11232-006-0008-6

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.

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