Standard

Homological properties of parafree Lie algebras. / Ivanov, Sergei O.; Mikhailov, Roman; Zaikovskii, Anatolii.

в: Journal of Algebra, Том 560, 15.10.2020, стр. 1092-1106.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Ivanov, SO, Mikhailov, R & Zaikovskii, A 2020, 'Homological properties of parafree Lie algebras', Journal of Algebra, Том. 560, стр. 1092-1106. https://doi.org/10.1016/j.jalgebra.2020.05.031

APA

Ivanov, S. O., Mikhailov, R., & Zaikovskii, A. (2020). Homological properties of parafree Lie algebras. Journal of Algebra, 560, 1092-1106. https://doi.org/10.1016/j.jalgebra.2020.05.031

Vancouver

Ivanov SO, Mikhailov R, Zaikovskii A. Homological properties of parafree Lie algebras. Journal of Algebra. 2020 Окт. 15;560:1092-1106. https://doi.org/10.1016/j.jalgebra.2020.05.031

Author

Ivanov, Sergei O. ; Mikhailov, Roman ; Zaikovskii, Anatolii. / Homological properties of parafree Lie algebras. в: Journal of Algebra. 2020 ; Том 560. стр. 1092-1106.

BibTeX

@article{0462ac590038493b95808dc2c2dadea6,
title = "Homological properties of parafree Lie algebras",
abstract = "In this paper, an explicit construction of a countable parafree Lie algebra 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 Z is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial H2.",
keywords = "Combinatorial group theory, Group homology, Lie algebras, Parafree conjecture, RELATIVELY FREE GROUP, LOWER CENTRAL SEQUENCE",
author = "Ivanov, {Sergei O.} and Roman Mikhailov and Anatolii Zaikovskii",
year = "2020",
month = oct,
day = "15",
doi = "10.1016/j.jalgebra.2020.05.031",
language = "English",
volume = "560",
pages = "1092--1106",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Homological properties of parafree Lie algebras

AU - Ivanov, Sergei O.

AU - Mikhailov, Roman

AU - Zaikovskii, Anatolii

PY - 2020/10/15

Y1 - 2020/10/15

N2 - In this paper, an explicit construction of a countable parafree Lie algebra 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 Z is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial H2.

AB - In this paper, an explicit construction of a countable parafree Lie algebra 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 Z is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial H2.

KW - Combinatorial group theory

KW - Group homology

KW - Lie algebras

KW - Parafree conjecture

KW - RELATIVELY FREE GROUP

KW - LOWER CENTRAL SEQUENCE

UR - http://www.scopus.com/inward/record.url?scp=85086871772&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2020.05.031

DO - 10.1016/j.jalgebra.2020.05.031

M3 - Article

AN - SCOPUS:85086871772

VL - 560

SP - 1092

EP - 1106

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 62108012