[{"_id":"63569","language":[{"iso":"eng"}],"user_id":"106729","year":"2025","title":"Describing the nub in maximal Kac-Moody groups","status":"public","author":[{"full_name":"Bischof, Sebastian","first_name":"Sebastian","last_name":"Bischof","id":"106729"},{"first_name":"Timothée","last_name":"Marquis","full_name":"Marquis, Timothée"}],"date_updated":"2026-01-12T14:33:08Z","external_id":{"arxiv":["arXiv:2508.15506"]},"date_created":"2026-01-12T14:12:09Z","type":"preprint","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"citation":{"chicago":"Bischof, Sebastian, and Timothée Marquis. “Describing the Nub in Maximal Kac-Moody Groups,” 2025.","short":"S. Bischof, T. Marquis, (2025).","apa":"Bischof, S., &#38; Marquis, T. (2025). <i>Describing the nub in maximal Kac-Moody groups</i>.","ieee":"S. Bischof and T. Marquis, “Describing the nub in maximal Kac-Moody groups.” 2025.","ama":"Bischof S, Marquis T. Describing the nub in maximal Kac-Moody groups. Published online 2025.","bibtex":"@article{Bischof_Marquis_2025, title={Describing the nub in maximal Kac-Moody groups}, author={Bischof, Sebastian and Marquis, Timothée}, year={2025} }","mla":"Bischof, Sebastian, and Timothée Marquis. <i>Describing the Nub in Maximal Kac-Moody Groups</i>. 2025."},"abstract":[{"lang":"eng","text":"Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction group $\\mathrm{con}(g)$ of an element $g\\in G$ is the set of all $h\\in G$ such that $g^n h g^{-n} \\to 1_G$ as $n \\to \\infty$. The nub of $g$ can then be characterized as the intersection $\\mathrm{nub}(g)$ of the closures of $\\mathrm{con}(g)$ and $\\mathrm{con}(g^{-1})$.\r\n Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that $\\mathrm{nub}(g) = \\{1\\}$ if and only if $\\mathrm{con}(g)$ is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem.\r\n Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups."}]},{"abstract":[{"lang":"eng","text":"In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings."}],"citation":{"bibtex":"@article{Bischof_2025, title={On flat groups in affine buildings}, author={Bischof, Sebastian}, year={2025} }","ama":"Bischof S. On flat groups in affine buildings. Published online 2025.","mla":"Bischof, Sebastian. <i>On Flat Groups in Affine Buildings</i>. 2025.","short":"S. Bischof, (2025).","chicago":"Bischof, Sebastian. “On Flat Groups in Affine Buildings,” 2025.","ieee":"S. Bischof, “On flat groups in affine buildings.” 2025.","apa":"Bischof, S. (2025). <i>On flat groups in affine buildings</i>."},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"preprint","date_created":"2026-01-12T14:11:47Z","external_id":{"arxiv":["arXiv:2512.16548"]},"date_updated":"2026-01-12T14:32:33Z","author":[{"full_name":"Bischof, Sebastian","first_name":"Sebastian","last_name":"Bischof","id":"106729"}],"status":"public","year":"2025","title":"On flat groups in affine buildings","user_id":"106729","_id":"63568","language":[{"iso":"eng"}]}]