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arXiv · 1710.01065

Representations of pure symmetric automorphism groups of RAAGs

Javier Aramayona·Conchita Martínez Pérez
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Abstract

We study representations of the pure symmetric automorphism group $PAut(A_Γ)$ of a RAAG $A_Γ$ with defining graph $Γ$. We first construct a homomorphism from $PAut(A_Γ)$ to the direct product of a RAAG and a finite direct product of copies of $F_2 \times F_2$; moreover, the image of $PAut(A_Γ)$ under this homomorphism is surjective onto each factor. As a consequence, we obtain interesting actions of $PAut(A_Γ)$ on non-positively curved spaces We then exhibit, for connected $Γ$, a RAAG which property contains $Inn(A_Γ)$ and embeds as a normal subgroup of $PAut(A_Γ)$. We end with a discussion of the linearity problem for $PAut(A_Γ)$.

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Javier Aramayona, Conchita Martínez Pérez. 2017-10-03. Representations of pure symmetric automorphism groups of RAAGs. https://arxiv.org/abs/1710.01065

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