Generalized Quaternions and Matrix Algebra
نویسندگان
چکیده
In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained complex matrices corresponding to basis of quaternions. Also, investigated features matrices. get Pauli Then, have shown that produced these is isomorphic Clifford Cl(E_αβ^3) space E_αβ^3.
 Finally, studied relations among symplectic group unit quaternions, unitary group, orthogonal group.
منابع مشابه
Generalized Quaternions
The quaternion group Q8 is one of the two non-abelian groups of size 8 (up to isomorphism). The other one, D4, can be constructed as a semi-direct product: D4 ∼= Aff(Z/(4)) ∼= Z/(4) o (Z/(4))× ∼= Z/(4) o Z/(2), where the elements of Z/(2) act on Z/(4) as the identity and negation. While Q8 is not a semi-direct product, it can be constructed as the quotient group of a semi-direct product. We wil...
متن کاملGeneralized quaternions and spacetime symmetriesa)
The construction of a class of associative composition algebras qn on R 4 generalizing the wellknown quaternions Q provides an explicit representation of the universal enveloping algebra of the real three-dimensional Lie algebras having tracefree adjoint representations (class A Bianchi type Lie algebras). The identity components of the four-dimensional Lie groups GL(qn,l) Cqn (general linear g...
متن کاملCubic Matrix, Generalized Spin Algebra and Uncertainty Relation
We propose a generalization of spin algebra using three-index objects. There is a possibility that a triple commutation relation among three-index objects implies a kind of uncertainty relation among their expectation values. E-mail: [email protected]
متن کاملDecompositions of Quaternions and Their Matrix Equivalents
Since quaternions have isomorphic representations in matrix form we investigate various well known matrix decompositions for quaternions.
متن کاملQuaternions and Biquaternions: Algebra, Geometry and Physical Theories
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and ”tensor” formulation of Q-units with their possible representations are discussed and groups of Q-units transformations leaving Q-multiplication rule form-invariant are determined. A series of mathematical and physical applications is offered, among...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fen ve mühendislik bilimleri dergisi
سال: 2023
ISSN: ['2147-5296', '2149-3367']
DOI: https://doi.org/10.35414/akufemubid.1182145