We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is ...the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.
In this article, we study the geometry of an infinite-dimensional hyperbolic space. We will consider the group of isometries of the Hilbert ball equipped with the Carathéodory metric and learn about ...some special subclasses of this group. We will also find some unitary equivalence condition and compute some cardinalities.
Homogeneous isosceles-free spaces Bargetz, Christian; Bartoš, Adam; Kubiś, Wiesław ...
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
2024/7, Letnik:
118, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called
isosceles-free
. In particular, we characterize all ...homogeneous isosceles-free spaces up to isometry as vector spaces over the two-element field, endowed with an injective norm. Using isosceles-free decompositions, we provide bounds on the maximal number of distances in arbitrary homogeneous finite metric spaces.
We compute the full isometry group of any left-invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such ...metrics and prove that the singularities of the moduli space of left-invariant metrics, up to isometric automorphism are contained in the subspace of classes of metrics with maximal index of symmetry.
The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the ...expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.
This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind ...its creation. It also concerns quantum linear groups, especially the coordinate ring of Mq(n) and the observation that K Mq(n) is a quadratic algebra, and can be equipped with a multiplier Hopf ∗-algebra structure in the sense of quantum permutation groups developed byWang and an observation by Rollier–Vaes. In our next paper, we will propose the study of multiplier Hopf graph algebras. The current paper can be viewed as a precursor to this upcoming work, serving as a crucial intermediary bridging the gap between the abstract concept of multiplier Hopf algebras and the well-developed field of graph theory, thereby establishing connections between them! This survey review paper is dedicated to the 78th birthday anniversary of Professor Alfons Van Daele.
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