Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies |
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Authors: | V V Gribanov V G Kadyshevsky A S Sorin |
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Institution: | (1) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia |
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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 describing these hierarchies in the framework
of the Hamiltonian formalism and constructing their first two Hamiltonian structures. We obtain the first Hamiltonian structure
for both bosonic and fermionic Lax operators and the second Hamiltonian structure only for bosonic Lax operators.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 90–102, January, 2006. |
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Keywords: | integrable systems Toda lattices R-matrix Yang-Baxter equation |
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