Lie Algebra of Unit Tangent Bundle in Minkowski 3-Space

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International Electronic Journal of Geometry
Volume:12 Issue:1
Lie Algebra of Unit Tangent Bundle in Minkowski 3-Space

Lie Algebra of Unit Tangent Bundle in Minkowski 3-Space

Pages : 1-8

View : 36 | Download : 12

Publication Date : 2019-03-27

Article Type : Research Paper

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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