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 -