Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

See all formats and pricing
More options …
Volume 29, Issue 3


Non-abelian tensor and exterior products of multiplicative Lie rings

Guram Donadze
  • Indian Institute of Science, Education and Research Thiruvananthapuram, 695016 Thiruvananthapuram, Kerala, India
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Nick Inassaridze
  • A. Razmadze Mathematical Institute of Tbilisi State University, Tamarashvili Str. 6, 0177 Tbilisi, Georgia; Georgian Technical University, Kostava Str. 77, 0175 Tbilisi, Georgia; and Tbilisi Centre for Mathematical Sciences, Tbilisi, Georgia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Manuel Ladra
  • Corresponding author
  • Department of Algebra, IMAT, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-08-18 | DOI: https://doi.org/10.1515/forum-2015-0096


We define a non-abelian tensor product of multiplicative Lie rings. This is a new concept providing a common approach to the non-abelian tensor product of groups defined by Brown and Loday and to the non-abelian tensor product of Lie rings defined by Ellis. We also prove an analogue of Miller’s theorem for multiplicative Lie rings.

Keywords: Multiplicative lie rings; non-abelian tensor and exterior products; homology

MSC 2010: 18G10; 18G50


  • [1]

    Bak A., Donadze G., Inassaridze N. and Ladra M., Homology of multiplicative Lie rings, J. Pure Appl. Algebra 208 (2007), no. 2, 761–777. Google Scholar

  • [2]

    Brown R. and Ellis G. J., Hopf formulae for the higher homology of a group, Bull. Lond. Math. Soc. 20 (1988), no. 2, 124–128. Google Scholar

  • [3]

    Brown R., Johnson D. L. and Robertson E. F., Some computations of non-abelian tensor products of groups, J. Algebra 111 (1987), no. 1, 177–202. Google Scholar

  • [4]

    Brown R. and Loday J.-L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311–335. Google Scholar

  • [5]

    Cohen D. E. and Lyndon R. C., Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537. Google Scholar

  • [6]

    Donadze G., Inassaridze N. and Porter T., N-fold Čech derived functors and generalised Hopf type formulas, J. K-Theory 35 (2005), no. 3–4, 341–373. Google Scholar

  • [7]

    Donadze G. and Ladra M., More on five commutator identities, J. Homotopy Relat. Struct. 2 (2007), no. 1, 45–55. Google Scholar

  • [8]

    Ellis G. J., Non-abelian exterior products of groups and exact sequences in the homology of groups, Glasg. Math. J. 29 (1987), no. 1, 13–19. Google Scholar

  • [9]

    Ellis G. J., Non-abelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras, J. Pure Appl. Algebra 46 (1987), no. 2–3, 111–115. Google Scholar

  • [10]

    Ellis G. J., The non-abelian tensor product of finite groups is finite, J. Algebra 111 (1987), no. 1, 203–205. Google Scholar

  • [11]

    Ellis G. J., A non-abelian tensor product of Lie algebras, Glasg. Math. J. 33 (1991), no. 1, 101–120. Google Scholar

  • [12]

    Ellis G. J., On five well-known commutator identities, J. Aust. Math. Soc. Ser. A 54 (1993), no. 1, 1–19. Google Scholar

  • [13]

    Inassaridze H., Non-Abelian Homological Algebra and its Applications, Math Appl. 421, Kluwer, Dordrecht, 1997. Google Scholar

  • [14]

    Miller C., The second homology group of a group; relations among commutators, Proc. Amer. Math. Soc. 3 (1952), 588–595. Google Scholar

  • [15]

    Point F. and Wantiez P., Nilpotency criteria for multiplicative Lie algebras, J. Pure Appl. Algebra 111 (1996), no. 1–3, 229–243. Google Scholar

About the article

Received: 2015-05-22

Revised: 2016-07-18

Published Online: 2016-08-18

Published in Print: 2017-05-01

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2013-43687-P

Funding Source: Shota Rustaveli National Science Foundation

Award identifier / Grant number: FR/189/5-113/14

Funding Source: Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia

Award identifier / Grant number: GRC2013-045

The authors were supported by Ministerio de Economía y Competitividad (Spain), grant MTM2013-43687-P (European FEDER support included). The first author was also partially supported by PEIN (USC-India) program. The second author was also supported by Shota Rustaveli National Science Foundation, grant FR/189/5-113/14. The third author was also supported by Xunta de Galicia (European FEDER support included), grant GRC2013-045.

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 563–574, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0096.

Export Citation

© 2017 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Ramji Lal and Sumit Kumar Upadhyay
Journal of Pure and Applied Algebra, 2018
G. Donadze, N. Inassaridze, M. Ladra, and A.M. Vieites
Journal of Pure and Applied Algebra, 2017
Guram Donadze, Xabier García-Martínez, and Emzar Khmaladze
Revista Matemática Complutense, 2017

Comments (0)

Please log in or register to comment.
Log in