Department of Applied Research,

Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv-4, UKRAINE

E-mail: spichak@imath.kiev.ua

**Invariance of Maxwell equations under nonlinear representations
of the Poincare algebra**

**Abstract:**

It is shown that the Maxwell equations are conditionally-invariant
with respect to two nonlinear representations of the Poincare algebra.
The corresponding groups of finite transformations are consructed. A nonlinear
generalization of the Maxwell equations, which is invariant under the above-mentioned
nonlinear representations of the Poincare algebra, is found.