Dirac matrices as elements of a superalgebraic matrix algebra

Elements of Matrix Algebra

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Dirac Gamma Matrices as Representations of the Algebra of Little Groups

The algebra of O(3, 3) is contracted to that of E(2)-like groups in the infinite-momentum limit. It is shown through this process that there are 18 different possibilities for the representations of E(2)-like algebra if they are to be expressed in terms of Dirac γmatrices. It is also pointed out that the generators of this algebra are independent of the particular representation of the γ-matric...

subgroups by using the Dirac matrix algebra basis

On unique parametrization of the linear group GL(4.C) and its subgroups by using the Dirac matrix algebra basis A unifying overview of the ways to parameterize the linear group GL(4.C) and its subgroups is given. As parameters for this group there are taken 16 coefficients G = G(A, B, A k , B k , F kl) in resolving matrix G ∈ GL(4.C) in terms of 16 basic elements of the Dirac matrix algebra. Al...

C*-Algebra numerical range of quadratic elements

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.