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- Title
LINEARITY PROBLEM FOR NON-ABELIAN TENSOR PRODUCTS.
- Authors
BARDAKOV, VALERIY G.; LAVRENOV, ANDREI V.; NESHCHADIM, MIKHAIL V.
- 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 ⊗H and tensor squares G ⊗ 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.
- Subjects
TENSOR products; NONABELIAN groups; KNOT groups; NILPOTENT groups; HOMOTOPY groups
- Publication
Homology, Homotopy & Applications, 2019, Vol 21, Issue 1, p269
- ISSN
1532-0073
- Publication type
Article
- DOI
10.4310/HHA.2019.v21.n1.a12