Lie Algebra of Unit Tangent Bundle


Bekar M., Yayli Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.27, no.2, pp.965-975, 2017 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s00006-016-0670-1
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.965-975
  • Keywords: Lie algebra, Planar displacement, Real-quaternion, Semi-quaternion, Unit tangent bundle, TRANSPOSITION ANTI-INVOLUTION, CLIFFORD

Abstract

In this paper, semi-quaternions are studied with their basic properties. Unit tangent bundle of is also obtained by using unit semi-quaternions and it is shown that the set of all unit semi-quaternions based on the group operation of semi-quaternion multiplication is a Lie group. Furthermore, the vector space matrix of angular velocity vectors forming the Lie algebra of the group is obtained. Finally, it is shown that the rigid body displacements obtained by using semi-quaternions correspond to planar displacements in .