A Comment on 'On the Rotation Matrix in Minkowski Space-time' by Ozdemir and Erdogdu

TL;DR

This paper discusses methods to derive the exponential map onto the Lorentz group, highlighting two elementary approaches involving algebraic structures and classical epimorphisms.

Contribution

It introduces two simple methods for obtaining the exponential map onto the Lorentz group, clarifying their mathematical foundations.

Findings

Two elementary methods for exponential map derivation

Use of conjugate semi-skew-symmetric matrices

Application of SL(2,C) to SO_0(3,1) epimorphism

Abstract

We comment on the article by M. Ozdemir and M. Erdogdu. We indicate that the exponential map onto the Lorentz group can be obtained in two elementary ways. The first way utilizes a commutative algebra involving a conjugate of a semi-skew-symmetric matrix, and the second way is based on the classical epimorphism from SL(2,C) onto SO_0(3,1)