FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 143-157

On the dimensions of commutative subalgebras and subgroups

M. V. Milentyeva

Abstract

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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.

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Last modified: June 17, 2006