Homological properties of parafree Lie algebras
| Autor: | Anatolii Zaikovskii, Sergei O. Ivanov, Roman Mikhailov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Parafree group Group Theory (math.GR) Mathematics - Rings and Algebras Homology (mathematics) Cohomological dimension 01 natural sciences Mathematics::Group Theory Rings and Algebras (math.RA) 0103 physical sciences Lie algebra FOS: Mathematics Countable set 010307 mathematical physics Finitely-generated abelian group 0101 mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Journal of Algebra. 560:1092-1106 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2020.05.031 |
| Popis: | In this paper, an explicit construction of a countable parafree Lie algebra over $\mathbb Z/2$ with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotent completion of a free noncyclic finitely generated Lie algebra over $\mathbb Z$ is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial $H_2$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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