Geodesic
Linearity problem for non-abelian tensor products
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 269-281.

Voir la notice de l'article provenant de la source International Press of Boston

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 $G \otimes H$ and tensor squares $G \otimes G$. 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.
DOI : 10.4310/HHA.2019.v21.n1.a12
Classification : 20E05, 20E25, 20G20
Keywords: non-abelian tensor product, linear group, faithful linear representation 
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     title = {Linearity problem for non-abelian tensor products},
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Valeriy G. Bardakov; Andrei V. Lavrenov; Mikhail V. Neshchadim. Linearity problem for non-abelian tensor products. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 269-281. doi : 10.4310/HHA.2019.v21.n1.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a12/

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