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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
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