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arXiv · 1408.1491

On the dimensions of commutative subalgebras and subgroups

Maria V. Milentyeva
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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 also get similar estimates for the dimension of a Lie group with bounded dimensions of its abelian Lie subgroups.

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Maria V. Milentyeva. 2014-08-07. On the dimensions of commutative subalgebras and subgroups. https://doi.org/10.1007/s10958-008-0052-x

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