This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary...This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.展开更多
We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated...We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated) twisted tensor products and L-R-twisted tensor products of algebras. Among the main results,we find the relations among these constructions. Furthermore, we study some properties of module twistors.展开更多
文摘This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.
基金supported by National Natural Science Foundation of China (Grant Nos. 11201285 and 11371238)the First-class Discipline of Universities in Shanghai
文摘We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated) twisted tensor products and L-R-twisted tensor products of algebras. Among the main results,we find the relations among these constructions. Furthermore, we study some properties of module twistors.
