Automorphisms of large-type free-of-infinity Artin groups (Q6668422)

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scientific article; zbMATH DE number 7972370
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Automorphisms of large-type free-of-infinity Artin groups
scientific article; zbMATH DE number 7972370

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    Automorphisms of large-type free-of-infinity Artin groups (English)
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    22 January 2025
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    Let \(A_{\Gamma}\) be the Artin group defined by the connected graph \(\Gamma=(V,E)\). The group \(A_{\Gamma}\) is said to be free-of-infinity if every pair of standard generators \(a,b \in V\) are adiacents.\N\NIn the paper under review, the author explicitly computes the automorphism and outer automorphism groups of all large-type, free-of-infinity Artin groups. A key consequence of the main theorem is that if \(A_{\Gamma}\) is a large-type, free-of-infinity Artin group, then \(\mathrm{Out}(A_{\Gamma}) \simeq \mathrm{Aut}(\Gamma) \times C_{2}\), and thus it is finite. The proof strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, meaning that it is independent of the choice of standard generators for the groups.
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    Artin group
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    automorphism
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    Deligne complex
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