相关论文: Quaternions for Guts
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…
We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.
In the paper [1] we consider a new class, so-called, $G$-monogenic (differentiable in the sense of Gateaux) quaternionic mappings. In the present paper we introduce quaternionic $H$-monogenic (differentiable in the sense of Hausdorff)…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
This work is devoted to the study of representations of finite subgroups of the group of units of quaternion division algebras over a global or local field arising from the inclusion via extension of scalars splitting the algebra. Following…
The purpose of this paper is to give presentations for projective $S$-unit groups of the Hurwitz order in Hamilton's quaternions over the rational field $\mathbb{Q}$. To our knowledge, this provides the first explicit presentations of an…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.
In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.
Capsules are grouping of neurons that allow to represent sophisticated information of a visual entity such as pose and features. In the view of this property, Capsule Networks outperform CNNs in challenging tasks like object recognition in…
We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar…
Constructive algorithms, requiring no more than $2\times 2$ matrix manipulations, are provided for finding the entries of the positive definite factor in the polar decomposition of matrices in sixteen groups preserving a bilinear form in…
We prove new fundamental lemma and arithmetic fundamental lemma identities for general linear groups over quaternion division algebras. In particular, we verify the transfer conjeture and the arithmetic transfer conjecture from…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and…
The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality…
Motivated by a problem of Halmos, we obtain a canonical decomposition for complex matrices which are unitarily equivalent to their transpose (UET). Surprisingly, the naive assertion that a matrix is UET if and only if it is unitarily…