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We give an introduction to the theory of pseudorepresentations of Taylor, Rouquier, Chenevier and Lafforgue. We refer to Taylor’s and Rouquier’s pseudorepresentations as pseudocharacters. They are very closely related, the main difference being that Taylor’s pseudocharacters are defined for a group, where as Rouquier’s pseudocharacters are defined for algebras. Chenevier’s pseudorepresentations are so-called polynomial laws and will be called determinant laws. Lafforgue’s pseudorepresentations are a generalization of Taylor’s pseudocharacters to other reductive groups G, in that the corresponding notion of representation is that of a G-valued representation of a group. We refer to them as G-pseudocharacters. We survey the known comparison theorems, notably Emerson’s bijection between Chenevier’s determinant laws and Lafforgue’s GL(n)-pseudocharacters and the bijection with Taylor’s pseudocharacters away from small characteristics. We show, that duals of determinant laws exist and are compatible with duals of representations. Analogously, we obtain that tensor products of determinant laws exist and are compatible with tensor products of representations. Further the tensor product of Lafforgue’s pseudocharacters agrees with the tensor product of Taylor’s pseudocharacters. We generalize some of the results of [Che14] to general reductive groups, in particular we show that the (pseudo)deformation space of a continuous Lafforgue G-pseudocharacter of a topologically finitely generated profinite group Γ with values in a finite field (of characteristic p) is noetherian. We also show, that for specific groups G it is sufficient, that Γ satisfies Mazur’s condition Φ_p. One further goal of this thesis was to generalize parts of [BIP21] to other reductive groups. Let F/Qp be a finite extension. In order to carry this out for the symplectic groups Sp2d, we obtain a simple and concrete stratification of the special fiber of the pseudodeformation space of a residual G-pseudocharater of Gal(F) into obstructed subloci Xdec(Θ), Xpair(Θ), Xspcl(Θ) of dimension smaller than the expected dimension n(2n + 1)[F : Qp]. We also prove that Lafforgue’s G-pseudocharacters over algebraically closed fields for possibly nonconnected reductive groups G come from a semisimple representation. We introduce a formal scheme and a rigid analytic space of all G-pseudocharacters by a functorial description and show, building on our results of noetherianity of pseudodeformation spaces, that both are representable and admit a decomposition as a disjoint sum indexed by continuous pseudocharacters with values in a finite field up to conjugacy and Frobenius automorphisms. At last, in joint work with Mohamed Moakher, we give a new definition of determinant laws for symplectic groups, which is based on adding a ’Pfaffian polynomial law’ to a determinant law which is invariant under an involution. We prove the expected basic properties in that we show that symplectic determinant laws over algebraically closed fields are in bijection with conjugacy classes of semisimple representation and that Cayley-Hamilton lifts of absolutely irreducible symplectic determinant laws to henselian local rings are in bijection with conjugacy classes of representations. We also give a comparison map with Lafforgue’s pseudocharacters and show that it is an isomorphism over reduced rings.

Dieses Buch dokumentiert 10 Jahre Risk-Governance-Forschung an der Universität Siegen. In 50 Beiträgen reflektieren Forscher und Praktiker Risk Governance vor dem Hintergrund ihrer eigenen Forschungen und/oder Erfahrungen und geben jeweils einen Entwicklungsimpuls für die Zukunft der Risk Governance. Das Buch zeigt die große Bandbreite und Tiefe des Forschungsgebietes auf und diskutiert Grundannahmen, Implementierungsfragen, die Rolle der Risk Governance als Transformationsmotor, ihre Wirkung in den verschiedenen betrieblichen Funktionen, Entwicklungsperspektiven und den Beitrag der Risk Governance zu einer nachhaltigen Ausrichtung von Unternehmen., This book documents 10 years of risk governance research at the University of Siegen. In 50 contributions, researchers and practitioners reflect on risk governance against the background of their own research and/or experience and provide a development impetus for the future of risk governance. The book shows the wide range and depth of the research field and discusses basic assumptions, implementation issues, the role of risk governance as transformation engine, its impact in the various operational functions, development perspectives, and the contribution of risk governance to a sustainable orientation of companies.

Unternehmen mit plattformbasiertem Geschäftsmodell lassen sich unter dem Begriff der Plattformökonomie subsumieren. Digitale Plattformen kennzeichnen sich dadurch, dass sie in der Regel als Vermittler agieren und einen digitalen Ort schaffen, der eine direkte soziale und wirtschaftliche Interaktion zwischen Anbietern und Nachfragern ermöglicht. Die Verbreitung digitaler Plattformen und der verstärkte Einfluss der Digitalisierung wirken sich auf das Verhalten und den Anspruch der Kunden an die Bank und deren Dienstleistungen aus. In der Wissenschaft sind die Potenziale der Plattformökonomie für Universalbanken bisher nicht hinreichend untersucht worden. Diese Dissertation zeigt auf, wie die Symbiose der Stärken traditioneller Universalbanken und der Potenziale der Plattformökonomie dazu beitragen kann, dass Banken ihre Rentabilität steigern und ihre Wettbewerbsposition stärken. Der Vertrieb von Bankdienstleistungen Dritter und die Vermittlung branchenfremder Dienstleistungen ermöglicht Universalbanken die Fokussierung auf ihre Kernkompetenzen und stellt zugleich sicher, dass ihren Kunden ein breites Angebotsspektrum offeriert wird. Die Vielzahl bestehender Kundenbeziehungen stellt dabei einen relevanten Wettbewerbsvorteil dar, der für die Implementierung einer digitalen Plattform genutzt werden kann. Die Untersuchung erarbeitet zunächst die Rahmenbedingungen der Plattformökonomie für Universalbanken und stellt die Anforderungen für den Einsatz von Plattformanwendungen in der Folge dar. Darauf aufbauend werden die Möglichkeiten der Ausgestaltung einer digitalen Plattform für Universalbanken erörtert., Companies with a platform-based business model can be subsumed under the term platform economy. Digital platforms are characterized by the fact that they usually act as intermediaries and create a digital place that enables direct social and economic interaction between suppliers and demanders. The proliferation of digital platforms and the increased influence of digitalization impact customers' interaction with and demand on the bank and its services. In science, the potentials of the platform economy for universal banks have not yet been sufficiently explored. This publication shows how the symbiosis of the strengths of traditional universal banks and the potentials of the platform economy can help banks to increase their profitability and strengthen their competitive position. The distribution of third-party banking services and the intermediation of services from outside the industry enable universal banks to focus on their core competencies while ensuring a broad range of services for their customers at the same time. The large number of existing customer relationships represents a key competitive advantage that can be used for the implementation of a digital platform. This PhD thesis first establish the framework conditions of a platform economy for universal banks and subsequently presents the requirements for the use of platform applications. Based on this, the possibilities of designing a digital platform for universal banks are discussed.