  We introduce and study soficity for Lie algebras, modelled after linear
soficity in associative algebras. We introduce equivalent definitions of
soficity, one involving metric ultraproducts and the other involving almost
representations. We prove that any Lie algebra of subexponential growth is
sofic. We also prove that a Lie algebra over a field of characteristic 0 is
sofic if and only if its universal enveloping algebra is linearly sofic.
Finally, we give explicit families of almost representations for the Witt and
Virasoro algebras.

Rings and Algebras