On the normalizers of subalgebras in an infinite Lie algebra. (English) Zbl 1078.35092
Summary: An algorithm for calculating the normalizer of a 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 obtained subalgebras. As an example, we consider the Lie symmetry algebra \(L\) admitted by the thermal diffusion equations. The first-order optimal system of subalgebras \(\Theta _{1}L\) is constructed and the normalizers of finite subalgebras from this system are found. The classification of subalgebras depending on arbitrary functions is made.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
Keywords:
Lie symmetry algebra; normalizer; optimal system of subalgebras; thermal diffusion equationSoftware:
PODMODELIReferences:
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