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1	Pairs in involution Halbig, Sebastian 08 August 2022 (has links) Pairs in involution are a Hopf algebraic structure with applications to category theory, cyclic homology and knot theory. In the present dissertation we will answer the question whether every finite-dimensional Hopf algebra admits such pairs, construct and investigate their categorical analogues, and develop, based on our previous findings, the theory of pairs in involutions for Hopf monads. info:eu-repo/classification/ddc/510 ddc:510
2	Mixed Witt rings of algebras with involution Garrel, Nicolas 04 April 2024 (has links) Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how tomultiply two ε-hermitian forms to obtain a quadratic form over the base field. This allows to define a commutative graded ring structure by taking together bilinear forms and ε-hermitian forms, which we call the mixedWitt ring of an algebra with involution. We also describe a less powerful version of this construction for unitary involutions, which still defines a ring, but with a grading over Z instead of the Klein group. We first describe a general framework for defining graded rings out of monoidal functors from monoidal categories with strong symmetry properties to categories of modules. We then give a description of such a strongly symmetric category Brₕ(K, ι) which encodes the usual hermitian Morita theory of algebras with involutions over a field K. We can therefore apply the general framework to Brₕ(K, ι) and theWitt group functors to define our mixed Witt rings, and derive their basic properties, including explicit formulas for products of diagonal forms in terms of involution trace forms, explicit computations for the case of quaternion algebras, and reciprocity formulas relative to scalar extensions. We intend to describe in future articles further properties of those rings, such as a λ-ring structure, and relations with theMilnor conjecture and the theory of signatures of hermitian forms. info:eu-repo/classification/ddc/510 ddc:510
3	On Infravacua and the Superselection Structure of Theories with Massless Particles / Über Infravakua und die Superauswahlstruktur von Theorien mit masselosen Teilchen Kunhardt, Walter 27 June 2001 (has links) No description available. 530 Physik Superauswahlsektoren Ladung masselose Teilchen langreichweitige Wechselwirkung monoidale Kategorien Infravakuum Vakuum Kozykel Lokalisierung superselection sectors charge massless particles long-range interaction monoidal catergories infravacuum vacuum cocycles localisation 33.24 EBID 100: Monoidal categories symmetric monoidal categories EIBT

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