Molev, A. I. On the growth of some Lie algebras of vector fields. (English. Russian original) Zbl 0607.17009 Russ. Math. Surv. 41, No. 2, 213-214 (1986); translation from Usp. Mat. Nauk 41, No. 2(248), 205-206 (1986). An asymptotic expression is given for the growth of the dimensions of homogeneous components of finitely generated subalgebras of the Lie algebra of all smooth vector fields on \({\mathbb{R}}^ m\) and (in the case of even m) of the Lie algebra of all Hamiltonian vector fields on \({\mathbb{R}}^ m\). Reviewer: Yu.N.Mukhin MSC: 17B70 Graded Lie (super)algebras 17B65 Infinite-dimensional Lie (super)algebras Keywords:asymptotic expression; growth; dimensions of homogeneous components; finitely generated subalgebras; Lie algebra; smooth vector fields; Hamiltonian vector fields PDF BibTeX XML Cite \textit{A. I. Molev}, Russ. Math. Surv. 41, No. 2, 213--214 (1986; Zbl 0607.17009); translation from Usp. Mat. Nauk 41, No. 2(248), 205--206 (1986) Full Text: DOI