On the dimensions of commutative subalgebras and subgroups |
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| Authors: | M V Milentyeva |
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| Institution: | (1) M. V. Lomonosov Moscow State University, Moscow |
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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 get similar estimates
for the dimension of a Lie group with bounded dimensions of its Abelian Lie subgroups.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 143–157, 2006. |
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