caa a22 4500 467910316 CHVBK 20180406152847.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s11232-006-0008-6 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0008-6 Hamiltonian Structures of Fermionic Two-Dimensional Toda Lattice Hierarchies [Elektronische Daten] [V. Gribanov, V. Kadyshevsky, A. Sorin] 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. Springer Science+Business Media, Inc., 2006 integrable systems nationallicence Toda lattices nationallicence R -matrix nationallicence Yang-Baxter equation nationallicence Gribanov V. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut Kadyshevsky V. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut Sorin A. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/1(2006-01-01), 73-84 0040-5779 146:1<73 2006 146 11232 https://doi.org/10.1007/s11232-006-0008-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0008-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gribanov V. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut NATIONALLICENCE 700 1- Kadyshevsky V. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut NATIONALLICENCE 700 1- Sorin A. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/1(2006-01-01), 73-84 0040-5779 146:1<73 2006 146 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer