Year: 2022
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Cinel, Cameron
Institution: University of California San Diego
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4293861397