Abstract
We study representations of the pure symmetric automorphism group PAut(AГ) of a RAAG AГ with defining graph Г.
We first construct a homomorphism from PAut(AГ) to the direct product of a RAAG and a finite direct product of copies of F2 × F2; moreover, the image of PAut(AГ) under this homomorphism is surjective onto each factor. As a consequence, we obtain interesting actions of PAut(AГ) on non-positively curved spaces
We then exhibit, for connected Г, a RAAG which properly contains Inn(AГ) and embeds as a normal subgroup of PAut(AГ). We end with a discussion of the linearity problem for PAut(AГ).
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The first named author is partially supported by RYC-2013-13008 and the second one by Gobierno de Aragón and European Regional Development Funds. Both authors were funded by grant MTM2015-67781.
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Aramayona, J., Martínez-Pérez, C. Representations of pure symmetric automorphism groups of RAAGs. Isr. J. Math. 232, 351–372 (2019). https://doi.org/10.1007/s11856-019-1875-5
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DOI: https://doi.org/10.1007/s11856-019-1875-5