Lie Algebra of Unit Tangent Bundle in Minkowski 3-Space

Year 2019, Volume: 12 Issue: 1, 1 - 8, 27.03.2019

Murat Bekar

https://doi.org/10.36890/iejg.545737

Abstract

In this paper, a one-to-one correspondence between the set of unit split semi-quaternions and

unit tangent bundle of semi-Euclidean plane is given. It is shown that the set of unit split semiquaternions

based on the group operation of multiplication is a Lie group. The Lie algebra of

this group, consisting of the vector space matrix of the angular velocity vectors, is also considered.

Planar rotations in Euclidean plane are expressed using split semi-quaternions. Some examples are

given to illustrate the findings.

Keywords

Lie algebra, pseudo-rotation (boost), split semi-quaternion, unit tangent bundle

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