Sofic Lie Algebras

Abstract: 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.

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algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar