On the dimensions of commutative subalgebras and subgroups
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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.
KeywordsAssociative Algebra Commutative Subalgebra Abelian Subalgebra Nilpotent Algebra Unital Associative Algebra
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