Lie algebras of finite subalgebra rank
For \(L\) a Lie algebra over a field \(F\), if \(d(H)\) denotes the minimal number of generators required to generate a subalgebra \(H\) of \(L\), then the subalgebra rank \(r\) of \(L\) is defined to be \(\sup \{d(H) | H\leq L\) and \(d(H)< \infty\}\), and \(L\) is said to be of finite rank if \(r<\infty\). The authors prove that if \(F\) has characteristic 0 or is algebraically closed with characteristic \(p\geq 5\), then every residually finite-dimensional Lie algebra of finite rank \(r\) has finite dimension bounded by an explicit function depending only on \(r\). Separate proofs are provided for the characteristic-zero and positive-characteristic cases.
residually finite-dimensional Lie algebra of finite rank
scientific article; zbMATH DE number 1145741