Computability and non-computability of equivalence for Lie structures that are pertinent to control theory

It is perhaps curious that the very extensive literature on decidability problems about isomorphism of like-type mathematical structures, ranging as it does from the consideration of such simple entities as monoids all the way up to differentiable manifolds and beyond, seems to contain little in the way of specific treatment of those well-known and tremendously useful middle-level objects, the Lie rings and Lie algebras. Thus, having run a "Mathfile" search, we have found only [1], [2], [3], and [4] as actually or potentially useful references, in this connection. Of course, our search was inherently impaired by the incompleteness of "Mathfile"; and was probably impaired somewhat by our choice of key words. Still, it is our subjective estimate that we likely turned up 20-25% of the extant, relevant literature. (Papers such as [5], too recent to be found on Mathfile, may of course also prove useful; [5], in particular, involves both explicit effectiveness considerations and some fairly subtle uses of polynomial-structure identities.)