TY - JOUR AB - A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups. AU - Glöckner, Helge AU - Willis, George A. ID - 34786 JF - Journal of Algebra KW - Contraction group KW - Torsion group KW - Extension KW - Cocycle KW - Section KW - Equivariant cohomology KW - Abelian group KW - Nilpotent group KW - Isomorphism types SN - 0021-8693 TI - Decompositions of locally compact contraction groups, series and extensions VL - 570 ER - TY - JOUR AU - Glöckner, Helge AU - Willis, George A. ID - 34790 JF - J. Reine Angew. Math. KW - 22D05 KW - 22A05 KW - 20E18 SN - 0075-4102 TI - Locally pro-p contraction groups are nilpotent VL - 781 ER - TY - JOUR AU - Glöckner, Helge ID - 34795 IS - 1 JF - Mathematische Nachrichten SN - 0025-584X TI - Direct limits of regular Lie groups VL - 294 ER - TY - GEN AB - Let $G$ be a Lie group over a totally disconnected local field and $\alpha$ be an analytic endomorphism of $G$. The contraction group of $\alpha$ ist the set of all $x\in G$ such that $\alpha^n(x)\to e$ as $n\to\infty$. Call sequence $(x_{-n})_{n\geq 0}$ in $G$ an $\alpha$-regressive trajectory for $x\in G$ if $\alpha(x_{-n})=x_{-n+1}$ for all $n\geq 1$ and $x_0=x$. The anti-contraction group of $\alpha$ is the set of all $x\in G$ admitting an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $x_{-n}\to e$ as $n\to\infty$. The Levi subgroup is the set of all $x\in G$ whose $\alpha$-orbit is relatively compact, and such that $x$ admits an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $\{x_{-n}\colon n\geq 0\}$ is relatively compact. The big cell associated to $\alpha$ is the set $\Omega$ of all all products $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and $z$ in the anti-contraction group. Let $\pi$ be the mapping from the cartesian product of the contraction group, Levi subgroup and anti-contraction group to $\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\Omega$ is open in $G$ and $\pi$ is \'{e}tale for suitable immersed Lie subgroup structures on the three subgroups just mentioned. Moreover, we study group-theoretic properties of contraction groups and anti-contraction groups. AU - Glöckner, Helge ID - 34806 T2 - arXiv:2101.02981 TI - Contraction groups and the big cell for endomorphisms of Lie groups over local fields ER - TY - CHAP AU - Zierau, Cornelia ED - Tahiri, Naima ED - Laasri, Mohammed ED - El Mtouni, Said ED - Jai-Mansouri, Rachid ID - 33746 T2 - Germanistik und DaF in mehrsprachigen Kontexten. Sprachdidaktische, interkulturelle und systemorientierte Perspektiven TI - „welt-strolch macht links-shreibreform“ – Sprach- und Kulturreflexionen mit literarischen Texten in den Studiengängen Deutsch als Fremd- und Zweitsprache am Beispiel des deutsch-brasilianischen Autors Zé do Rock ER - TY - JOUR AB - Nowadays, the production of modern lightweight structures, like a body in white structure requires a wide variety of mechanical joining processes. To fulfill the various demands, mechanical joining processes and joining elements (JE) are used. Very often, they are adapted to the application, which leads in turn to a numerous of different variants, high costs, and loss of the process chain versatility. To overcome this drawback, an innovative approach is the usage of individually produced and task-adapted JE, the so-called friction spun joint connectors (FSJC). These connectors can be modified in shape as well as in material properties. This flexibility offers high potential for lightweight design but also increases the necessary analytical effort regarding the forming process as well as the manufactured joint's properties. Therefore, a new analysis strategy based on the Finite-Element-Method (FEM) is proposed, which numerically determines the local load bearing capacity within a given joint in order to identify the critical regions for load transfer. The process of joining element manufacturing and the analysis strategy will be described in detail and optimization results of the joints are shown. Numerical results are discussed and possible recommendations for joint manufacturing are derived. AU - Wischer, Christian AU - Steinfelder, Christian AU - Homberg, Werner AU - Brosius, Alexander ID - 30649 JF - IOP Conference Series: Materials Science and Engineering TI - Joining with Friction Spun Joint Connectors – Manufacturing and Analysis VL - 1157 ER - TY - JOUR AU - Wischer, Christian AU - Homberg, Werner ID - 30702 JF - Production Engineering TI - A contribution on versatile process chains: joining with adaptive joining elements, formed by friction spinning ER - TY - GEN AU - Süßmann, Johannes ED - Butzer, Günter ED - Jacob, Joachim ID - 35027 SN - 978-3-476-04944-5 T2 - Metzler Lexikon literarischer Symbole TI - [Art.] Donau ER - TY - GEN AU - Süßmann, Johannes ID - 35066 TI - Mariemont – Modernismus und Erinnerung. Videographierter Vortrag für den 5. Belgientag des Belgienzentrums Paderborn ›Belgien – Pralle Kunst des Lebens‹ am 18. Mai 2021 ER - TY - GEN AU - Süßmann, Johannes ED - Jacob, Joachim ED - Süßmann, Johannes ID - 34980 SN - 978-90-04-33935-4 T2 - The Reception of Antiquity in the Age of Enlightenment. English Edition ed. by Christina C. Harker. Translated by Duncan Alexander Smart TI - [Art.] Greek/Roman antithesis VL - 12 ER -