Journal of Mathematical Sciences

, Volume 149, Issue 2, pp 1135–1145 | Cite as

On the dimensions of commutative subalgebras and subgroups



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.


Associative Algebra Commutative Subalgebra Abelian Subalgebra Nilpotent Algebra Unital Associative Algebra 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscow

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