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Linearity problem for non-abelian tensor products. / Bardakov, Valeriy G.; Lavrenov, Andrei V.; Neshchadim, Mikhail V.

In: Homology, Homotopy and Applications, Vol. 21, No. 1, 01.01.2019, p. 269-281.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, VG, Lavrenov, AV & Neshchadim, MV 2019, 'Linearity problem for non-abelian tensor products', Homology, Homotopy and Applications, vol. 21, no. 1, pp. 269-281. https://doi.org/10.4310/HHA.2019.v21.n1.a12

APA

Bardakov, V. G., Lavrenov, A. V., & Neshchadim, M. V. (2019). Linearity problem for non-abelian tensor products. Homology, Homotopy and Applications, 21(1), 269-281. https://doi.org/10.4310/HHA.2019.v21.n1.a12

Vancouver

Bardakov VG, Lavrenov AV, Neshchadim MV. Linearity problem for non-abelian tensor products. Homology, Homotopy and Applications. 2019 Jan 1;21(1):269-281. doi: 10.4310/HHA.2019.v21.n1.a12

Author

Bardakov, Valeriy G. ; Lavrenov, Andrei V. ; Neshchadim, Mikhail V. / Linearity problem for non-abelian tensor products. In: Homology, Homotopy and Applications. 2019 ; Vol. 21, No. 1. pp. 269-281.

BibTeX

@article{77da5688c66b4591939616545401161f,
title = "Linearity problem for non-abelian tensor products",
abstract = "In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products G circle times H and tensor squares G circle times G. Using these results we prove that tensor squares of some groups with one relation and some knot groups are linear. We prove that the Peiffer square of a finitely generated linear group is linear. At the end we construct faithful linear representations for the non-abelian tensor square of a free group and free nilpotent group.",
keywords = "Faithful linear representation, Linear group, Non-abelian tensor product, non-abelian tensor product, linear group, faithful linear representation",
author = "Bardakov, {Valeriy G.} and Lavrenov, {Andrei V.} and Neshchadim, {Mikhail V.}",
year = "2019",
month = jan,
day = "1",
doi = "10.4310/HHA.2019.v21.n1.a12",
language = "English",
volume = "21",
pages = "269--281",
journal = "Homology, Homotopy and Applications",
issn = "1532-0073",
publisher = "International Press of Boston, Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Linearity problem for non-abelian tensor products

AU - Bardakov, Valeriy G.

AU - Lavrenov, Andrei V.

AU - Neshchadim, Mikhail V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products G circle times H and tensor squares G circle times G. Using these results we prove that tensor squares of some groups with one relation and some knot groups are linear. We prove that the Peiffer square of a finitely generated linear group is linear. At the end we construct faithful linear representations for the non-abelian tensor square of a free group and free nilpotent group.

AB - In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products G circle times H and tensor squares G circle times G. Using these results we prove that tensor squares of some groups with one relation and some knot groups are linear. We prove that the Peiffer square of a finitely generated linear group is linear. At the end we construct faithful linear representations for the non-abelian tensor square of a free group and free nilpotent group.

KW - Faithful linear representation

KW - Linear group

KW - Non-abelian tensor product

KW - non-abelian tensor product

KW - linear group

KW - faithful linear representation

UR - http://www.scopus.com/inward/record.url?scp=85057744546&partnerID=8YFLogxK

U2 - 10.4310/HHA.2019.v21.n1.a12

DO - 10.4310/HHA.2019.v21.n1.a12

M3 - Article

AN - SCOPUS:85057744546

VL - 21

SP - 269

EP - 281

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 1

ER -

ID: 17828121