|XXXV Workshop on Geometric Methods in Physics
Construction of Lie algebra realizations
The problem of realization of a Lie algebra structure by vector fields
is widely applicable in group analysis of differential equations. One
of the natural problems arising is classification of all realizations
of a given Lie algebra. It is known, that classification of so called
transitive realizations is equivalent to classification of subalgebras
of the Lie algebra. In the presentation we briefly introduce one of
possible ways of constructing transitive realizations proposed by A. A.
Magazev, V. V. Mikheyev and I. V. Shirokov. Then we shall discuss
possible ways of construction of non-transitive realizations.