ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 30G35, 31B05, 41A10 Krasnov, Yakov, Bar-Ilan University, Israel Symmetries of Cauchy-Riemann-Füter Equation. The Cauchy-Riemann-Füter (CRF) equation [1] is a system of first order elliptic partial differential equations in quaternionic space H : Df := ∂_{x_{0}}f + i∂_{x_{1}}f +j∂_{x_{2}}f +k∂_{x_{3}}f = 0. We build the Lie algebra of all first order partial differential symmetries operators for a CRF equations and show a technique of the symmetry operators for a constructing all their solutions. Reference: [1] R. Füter, Analytische Funktionen einer Quaternionen Variablen, Comment Math. Helv. , 1932, v.4, pp. 9-20.