Year: 2025
Type: article
Abstract: Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras. Namely, we investigate obstacles to rank-approximation of “almost” solutions by exact solutions to systems of polynomial equations. This leads to a rich theory of stable associative and Lie algebras, with connections to linear soficity, amenability, growth, and group stability. We develop rank-stability and instability criteria, examine the effect of algebraic constructions on rank-stability, and prove that while finite-dimensional associative algebras are rank-stable, “most” finite-dimensional Lie algebras are not.
DOI: 10.1093/imrn/rnaf173
Authors: Tomer Bauer, Guy Blachar, Be’eri Greenfeld
Institutions: Bar-Ilan University, University of Washington
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4412006233