Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations

In this Letter we establish the correspondence between Bogoyavlenskij symmetries [Phys. Lett. A. 291 (4-5) (2001) 256, Phys. Rev. E. 66 (5) (2002) 056410] of the MHD equilibrium equations and Lie point transformations of these equations. We show that certain non-trivial Lie point transformations (that are obtained by direct application of Lie method) are equivalent to Bogoyavlenskij symmetries