Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies
Abstract
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.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- January 2006
- DOI:
- 10.1007/s11232-006-0008-6
- arXiv:
- arXiv:nlin/0505039
- Bibcode:
- 2006TMP...146...73G
- Keywords:
-
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Mathematical Physics
- E-Print:
- 12 pages, LaTeX, the talks delivered at the International Workshop on Classical and Quantum Integrable Systems (Dubna, January 24 - 28, 2005) and International Conference on Theoretical Physics (Moscow, April 11 - 16, 2005)