Related papers: Some remarks regarding Quaternions and Octonions
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…
This paper is devoted to survey composition algebras and some of their applications. After overviewing the classical algebras of quaternions and octonions, both unital composition algebras (or Hurwitz algebras) and symmetric composition…
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
We present Capelli type identities associated with the quaternions and the octonions, which are noncommutative versions of multiplicative norm identities for the quaternions and the octonions.
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
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…
This study investigates the theoretical and computational aspects of quaternion generalized inverses, focusing on outer inverses and {1,2}-inverses with prescribed range and/or null space constraints. In view of the non-commutative nature…
M\"obius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
In this study, we introduce a new class of quaternions associated with the well-known modified third-order Jacobsthal numbers. There are many studies about the quaternions with special integer sequences and their generalizations. All of…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with…
The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe…
A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie…
In this paper we show how generalized quaternions, including 2X2 matrices, can be used to find solutions of a non-commuting equation intimately connected with braid groups. These solutions can then be used to find polynomial invariants of…
This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups…
The quaternionic description of semiconductor single-electron devices is given in the single-electron regime. The conversion scheme of complex value Hamiltonian into a quaternion is formulated for the case of single-electron semiconductor…