We introduce a notion of soficity for Lie algebras, similar to linear soficity for groups and associative algebras. Sofic Lie algebras can be thought of as Lie algebras that locally are almost embeddable in \(\mathfrak{gl}_n(F)\) for some \(n\). We provide equivalent characterizations for soficity via metric ultraproducts and local \(\varepsilon\)-almost representations. We show that Lie algebras of subexponential growth are sofic and give explicit families of almost representations for specific Lie algebras. Finally we show that, over fields of characteristic 0, a Lie algebra is sofic if and only if its universal enveloping algebra is linearly sofic.
Join Zoom meeting ID 641 2123 2568 or via the link below. Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)