Finite Lorentz transformations, automorphisms, and division algebras

Finite generation of division subalgebras and of the group of eigenvalues for commuting derivations or automorphisms of division algebras

Let D be a division algebra such that D ⊗ D is a Noetherian algebra, then any division subalgebra of D is a finitely generated division algebra. Let ∆ be a finite set of commuting derivations or automorphisms of the division algebra D, then the group Ev(∆) of common eigenvalues (i.e. weights) is a finitely generated abelian group. Typical examples of D are the quotient division algebra Frac(D(X...

On Automorphisms of Order Three of Division Algebras*

Let A be a finite dimensional division algebra (not necessarily associative) over a field. The automorphisms of A having order three are characterized by giving a canonical matrix representation for each of the possible types (there are three). Examples are given to show that each type does exist. Some general results concerning automorphisms of prime power order are included.

Lorentz Transformations

In these notes we study Lorentz transformations and focus on the group of proper, orthochronous Lorentz transformations, donated by L+. (These Lorentz transformations have determinant one and preserve the direction of time.) The 2×2 matrices with determinant one, denoted SL(2, C), play a key role, as there is a map from SL(2,C) onto L+, that is 2-to-1 and a homomorphism. In this correspondence,...

Lorentz Transformations and Statistical Mechanics

In [Gottlieb (1998)] and [Gottlieb (2000)] we launched a study of Lorentz transformations. We find that every Lorentz transformation can be expressed as an exponential e where F is a skew symmetric operator with respect to the Minkowski metric 〈 , 〉 of form −+++. We provided F with the notation of electromagnetism. Thus we can describe boosts as pure ~ E fields and rotations as pure ~ B fields....

Automorphisms of Operator Algebras