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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


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Volume 29, Issue 3

Issues

Non-abelian tensor and exterior products of multiplicative Lie rings

Guram Donadze
  • Indian Institute of Science, Education and Research Thiruvananthapuram, 695016 Thiruvananthapuram, Kerala, India
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/ 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
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/ Manuel Ladra
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  • Department of Algebra, IMAT, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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Published Online: 2016-08-18 | DOI: https://doi.org/10.1515/forum-2015-0096

Abstract

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

References

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    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

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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.

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