Lie Algebra of Unit Tangent Bundle

Bekar M., YAYLI Y.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00006-016-0670-1
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.965-975
  • Anahtar Kelimeler: Lie algebra, Planar displacement, Real-quaternion, Semi-quaternion, Unit tangent bundle, TRANSPOSITION ANTI-INVOLUTION, CLIFFORD
  • Ankara Üniversitesi Adresli: Evet

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 .