Argument shift method

In mathematics, the argument shift method is a method for constructing functions in involution with respect to Poisson–Lie brackets, introduced by Mishchenko and Fomenko (1978). They used it to prove that the Poisson algebra of a finite-dimensional semisimple Lie algebra contains a complete commuting set of polynomials.

References

• Mishchenko, A. S.; Fomenko, A. T. (1978), "Euler equation on finite-dimensional Lie groups", Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian), 42 (2): 396–415, ISSN 0373-2436, MR 0482832 English translation: Math. USSR-Izv. 12 (1978), no. 2, 371–389