Rigidity of free algebras in varieties of lie algebras |
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| Authors: | Y. Bahturin D. Pagon M. Zaicev |
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| Affiliation: | 1. Department of algebra , Moscow State University , Moscow, 119899, RussiaFaculty of mathematics and mechanics;2. Pedagogical Faculty , University of Maribor , Koroska Cesta, Maribor, 24, Slovenia |
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| Abstract: | In this paper the main result is the rigidity of varietally free Lie algebras within the varieties where they are free. In fact, these algebras are usually free in some larger varieties, such as various types of the commutator varieties, and this is demonstrated in this paper as well. A related paper is [2] where, among some other results, we claimed the rigidity of free metabelian algebras within the respective variety of Lie algebras. |
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