The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra
Blackmore, Denis ; Prykarpatsky, Yarema A. ; Samulyak, Roman
arXiv, 9801203 / Harvested from arXiv
Text on arXiv
We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation.
Publié le : 1997-12-31
Classification:  Mathematical Physics 
@article{9801203,
     author = {Blackmore, Denis and Prykarpatsky, Yarema A. and Samulyak, Roman},
     title = {The integrability of Lie-invariant geometric objects generated by ideals
  in the Grassmann algebra},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9801203}
}

Blackmore, Denis; Prykarpatsky, Yarema A.; Samulyak, Roman. The integrability of Lie-invariant geometric objects generated by ideals
  in the Grassmann algebra. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9801203/