Lie Algebra of Unit Tangent Bundle


Bekar M. , Yayli Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.27, sa.2, ss.965-975, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 27 Konu: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00006-016-0670-1
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Sayfa Sayıları: ss.965-975

Özet

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 .