Article
Mathematics, Applied
Miguel Barrero
Summary: Global transfer systems are equivalent to global N infinity-operads, which categorize different levels of commutativity in globally equivariant homotopy theory, where objects have compatible actions by all compact Lie groups. This paper explicitly describes and completely classifies global transfer systems.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Ethan M. Ackelsberg
Summary: This paper focuses on the rigidity phenomenon for measure preserving actions of countable discrete abelian groups and its interaction with weak mixing and recurrence. The results about Z-actions are extended to this setting, showing the properties of rigidity sequences in weakly mixing systems and sets of recurrence. While techniques for Z-actions play a key role, additional ideas are introduced for dealing with groups with multiple generators.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo
Summary: This passage introduces the concept of conditional coproduct in the category of abelian pro-Lie groups. It shows that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.
MONATSHEFTE FUR MATHEMATIK
(2023)
Article
Mathematics
Lucas C. Lopes, Pavel Shumyatsky, Pavel A. Zalesskii
Summary: We generalize the definition of a finite A-group to profinite groups and provide a description of profinite A-groups as a triple semidirect product of two prosoluble groups with a semisimple group, extending an earlier result of A. M. Broshi to the profinite case. We also prove that a profinite A-group with a finitely generated non-trivial Fitting subgroup is metabelian-by-(finite exponent). Additionally, if G is finitely generated, it is virtually metabelian polycyclic.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics, Applied
Anna Fino, Fabio Paradiso
Summary: We study left-invariant generalized Kahler structures on almost abelian Lie groups and classify six-dimensional almost abelian Lie groups with a left-invariant complex structure. We also determine the six-dimensional compact almost abelian solvmani-folds admitting an invariant generalized Kahler structure. Additionally, we prove results related to holomorphic Poisson structures and pluriclosed flow.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2021)
Article
Mathematics
Zhicheng Wang
Summary: This paper investigates the Gan-Gross-Prasad problem for finite classical groups, providing complete answers for unipotent representations and obtaining explicit branching laws for these representations. Additionally, a formula is presented to simplify the Gan-Gross-Prasad problem to the restriction problem of Deligne-Lusztig characters for arbitrary representations.
ADVANCES IN MATHEMATICS
(2021)
Article
Chemistry, Multidisciplinary
Javier Gonzalez-Platas, Nebil A. Katcho, Juan Rodriguez-Carvajal
Summary: The Hall symbols have been extended to describe any setting of the 1651 types of magnetic space groups, with a computer program called MHall developed to parse the symbols, generate the full list of symmetry operators, and identify the transformation to the standard setting.
JOURNAL OF APPLIED CRYSTALLOGRAPHY
(2021)
Article
Mathematics
Wei He, Dekui Peng
Summary: The paper introduces the concept of m-normal subgroups and their relationship to Lie groups in locally compact and compact groups. The application extends a theorem on lower continuity for dense subgroups of arbitrary topological groups, showing that lower continuity is preserved under taking topological products. It is also demonstrated that an infinite compact group is hereditarily lower continuous if and only if the normalizer of every non-trivial finite subgroup is finite.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics
A. Savini
Summary: We introduce the concept of pullback along a measurable cocycle and extend the studied Borel invariant to the realm of measurable cocycles. The Borel invariant remains constant along cohomology classes and has a bounded absolute value, allowing for the definition of maximal cocycles. It is then proven that maximal cocycles are actually trivializable to the restriction of the irreducible representation.
JOURNAL OF TOPOLOGY AND ANALYSIS
(2022)
Article
Mathematics
Andrey R. Chekhlov, Peter Danchev, Brendan Goldsmith
Summary: An object is considered Bassian if it cannot be embedded in a proper homomorphic image of itself. In this study on Abelian groups, a complete characterization of all such groups is achieved based on their associated torsion-free and p-primary ranks.
ARCHIV DER MATHEMATIK
(2021)
Article
Mathematics, Applied
Sergio Cacciatori, Pietro Ursino
Summary: This paper studies the phenomenon of concentration of measures in families of compact connected Lie groups. It provides explicit examples for the determination of the region where the measure concentrates, using Macdonald's formula and Ricci curvature analysis.
Article
Mathematics, Applied
Rohollah Bakhshandeh-Chamazkoti
Summary: The aim of this paper is to investigate the non-isometric left-invariant Lorentz metrics on four-dimensional nilpotent Lie groups H-3 x R and G(4) that satisfy the Ricci soliton equation.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Clotilde Fermanian Kammerer, Veronique Fischer, Steven Flynn
Summary: In this paper, the effects of the pull-back by diffeomorphisms on pseudodifferential operators in the semi-classical setting constructed on nilpotent graded Lie groups are analyzed. It is proved that diffeomorphisms that preserve the filtration are uniformly Pansu differentiable. It is shown that the pull-back of a semi-classical pseudodifferential operator by such a diffeomorphism has a semi-classical symbol expressed at leading order in terms of the Pansu differential. Finally, the geometric meaning of this invariance in the setting of filtered manifolds is interpreted.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Eva Bayer-Fluckiger, Uriya A. First, Raman Parimala
Summary: In this paper, we prove new cases of the Grothendieck-Serre conjecture for classical groups by constructing a new Gersten-Witt complex for Witt groups of Azumaya algebras with involution. The complex is shown to be exact under certain conditions.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
(2022)
Article
Mathematics
Fausto De Mari
Summary: This paper investigates locally soluble groups with restrictions on subgroups which are neither abelian nor self-normalizing.
ARCHIV DER MATHEMATIK
(2022)
