This article is cited in 5 papers

On the dimensions of commutative subalgebras and subgroups

M. V. Milentyeva

M. V. Lomonosov Moscow State University

Abstract: We consider the functions that bound the dimensions of finite-dimensional associative or Lie algebras in terms of the dimensions of their commutative subalgebras. It is proved that these functions have quadratic growth. As a result, we get similar estimates for the dimension of a Lie group with bounded dimensions of its Abelian Lie subgroups.

UDC: 512.812.4+512.552

 English version: Journal of Mathematical Sciences (New York), 2008, 149:2, 1135–1145

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