On the normalizers of subalgebras in an infinite Lie algebra

An algorithm for calculating the normalizer of subalgebra in an infinite Lie symmetry algebra is proposed. The classification problem for a subalgebra spanned by generators that depend on arbitrary functions is formulated. This problem lies in finding the specifications of arbitrary functions and calculating the normalizers of the subalgebras so obtained. As an example, we consider the Lie symmetry algebra L admitted by the thermal diffusion equations. The first-order optimal system of subalgebras Θ1L is constructed and the normalizers of finite subalgebras from this system are found. The classification of subalgebras depending on arbitrary functions is made.