Argument shift method: Difference between revisions

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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, 42 (2): 396–415, ISSN 0373-2436, MR0482832 English translation: Math. USSR-Izv. 12 (1978), no. 2, 371–389

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-In mathematics, the '''argument shift method''' was introduced by {{harvs|txt|last1=Mishchenko|last2=
+In mathematics, the '''argument shift method''' is a method for constructing functions in involution with respect to [[Poisson–Lie bracket]]s, introduced by {{harvs|txt|last1=Mishchenko|last2=
-Fomenko|year=1978}} who used it to prove that the [[Poisson algebra]] of a finite-dimensional [[semisimple Lie algebra]] contains a complete commuting set of polynomials.
+Fomenko|year=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==