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 -