Multidimensional integrable systems from deformations of Lie algebra homomorphisms
نویسنده
چکیده
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti–self–dual Yang–Mills equations with a gauge group Diff(S). email [email protected] email [email protected] email [email protected]
منابع مشابه
Multidimensional integrable systems and deformations of Lie algebra homomorphisms
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti–self–dual Yang–Mills equations with a gauge group Diff(S). email [email protected] email [email protected] email [email protected]
متن کاملOn Some Class of Multidimensional Nonlinear Integrable Systems A
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed. 1. In the report we give a Lie algebraic and differential geometry derivation of a wide class of nonlinear integrable systems of partial differential equations for the functions depending on an arbit...
متن کاملOn the Liouville-Arnold integrable flows related with quantum algebras and their Poissonian representations
Based on the structure of Casimir elements associated with general Hopf algebras there are constructed Liouville-Arnold integrable flows related with naturally induced Poisson structures on arbitrary co-algebra and their deformations. Some interesting special cases including the oscillatory Heisenberg-Weil algebra related co-algebra structures and adjoint with them integrable Hamiltonian system...
متن کاملQuantum (1+1) extended Galilei algebras: from Lie bialgebras to quantum R-matrices and integrable systems
The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and classified into four multiparametric families. Their quantum deformations are obtained, together with the corresponding deformed Casimir operators. For the coboundary cases quantum universal R-matrices are also given. Applications of the quantum extended Galilei algebras to classical integrable systems are explicitly deve...
متن کاملA systematic construction of completely integrable Hamiltonians from coalgebras
A universal algorithm to construct N -particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of Hamiltonian systems with coalgebra symmetry. In order to illustrate this g...
متن کامل