Left Bol loops with the A ℓ-property or gyrogroups are generalization of groups which do not
explicitly have associativity. In this work, we define topological gyrogroups and study some …

Using the Clifford algebra formalism, we show that the unit ball of a real inner product space
equipped with Einstein addition forms a uniquely 2-divisible gyrocommutative gyrogroup or …

A Lorentz transformation group SO (m, n) of signature (m, n), m, n∈ N, in m time and n
space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of …

In this paper we propose to develop harmonic analysis on the Poincaré ball B _ t^ n B tn, a
model of the n n-dimensional real hyperbolic space. The Poincaré ball B _ t^ n B tn is the …

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified
study of the Lorentz transformation group SO (m, n) of signature (m, n), m, n? N, which is fully …

Within the framework of differential geometry, we study binary operations in the open, unit
ball of the Euclidean n-space R n, n∈ N, and discover the properties that qualify these …

The decomposition $\Gamma= BH $ of a group $\Gamma $ into a subset $ B $ and a
subgroup $ H $ of $\Gamma $ induces, under general conditions, a group-like structure for …

In this paper we make an attempt to study right loops (S, o) in which, for each y∈ S, the map
σ y from the inner mapping group GS of (S, o) to itself given by σ y (h)(x) oh (y)= h (xoy), x∈ …

In this paper, we study gyro-groups associated to groups, group extensions admitting gyro-
sections, and corresponding co-homologies. We also describe the obstructions in terms of …

Recently discovered tools to study analytic hyperbolic geometry in terms of analogies with
analytic Euclidean geometry are presented and employed. Special attention is paid to the …