Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 011, 19 pages      arXiv:0802.0184      http://dx.doi.org/10.3842/SIGMA.2008.011
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Classical R-Operators and Integrable Generalizations of Thirring Equations

Taras V. Skrypnyk a, b
a) SISSA, via Beirut 2-4, 34014 Trieste, Italy
b) Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., Kyiv 03680, Ukraine

Received October 31, 2007, in final form January 18, 2008; Published online February 01, 2008

Abstract
We construct different integrable generalizations of the massive Thirring equations corresponding loop algebras gσ in different gradings and associated ''triangular'' R-operators. We consider the most interesting cases connected with the Coxeter automorphisms, second order automorphisms and with ''Kostant-Adler-Symes'' R-operators. We recover a known matrix generalization of the complex Thirring equations as a partial case of our construction.

Key words: infinite-dimensional Lie algebras; classical R-operators; hierarchies of integrable equations.

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