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On the Dimensions of Commutative Subalgebras and Subgroups of Nilpotent Algebras and Lie Groups of Class 2 |
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| Authors: | Maria V Milentyeva |
| Institution: | 1. Higher Algebra, Department of Mechanics and Mathematics , M. V. Lomonosov Moscow State University , Leninskie Gory, Moscow mariamil@yandex.ru |
| Abstract: | We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also compute a similar function for complex nilpotent Lie groups of class 2. |
| Keywords: | Commutative (Abelian) Lie subgroups Commutative (Abelian) subalgebras Dimension Nilpotent associative algebra of class 2 Nilpotent Lie algebra of class 2 Nilpotent Lie group of class 2 |