On the dimensions of commutative subalgebras and subgroups. (Q950836)
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| Language | Label | Description | Also known as |
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| English | On the dimensions of commutative subalgebras and subgroups. |
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On the dimensions of commutative subalgebras and subgroups. (English)
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28 October 2008
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The author considers 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, the author obtains similar estimates for the dimension of a Lie group with bounded dimensions of its Abelian Lie subgroups. The author obtains estimates for the fields \(\mathbb{C}\), \(\mathbb{R}\), and an arbitrary field of characteristic zero as well.
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commutative subalgebras
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Lie algebras
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associative algebras
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Lie groups
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