Involutions in split semi-quaternions

BEKAR M., YAYLI Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.41, sa.12, ss.4491-4505, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 12
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/mma.4910
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4491-4505
  • Anahtar Kelimeler: (anti)-involution, hyperbolic-isoclinic rotation, planar rotation, split semi-quaternion, TRANSPOSITION ANTI-INVOLUTION, CLIFFORD
  • Ankara Üniversitesi Adresli: Evet

Özet

A map is an involution (resp, anti-involution) if it is a self-inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi-quaternions can be used to express half-turn planar rotations in 3-dimensional Euclidean space R3 and how they can be used to express hyperbolic-isoclinic rotations in 4-dimensional semi-Euclidean space R3,1. We present an involution and an anti-involution map using split semi-quaternions and give their geometric interpretations as half-turn planar rotations in R3. Also, we give the geometric interpretation of nonpure unit split semi-quaternions, which are in the form p = cosh + sinhi + 0j + 0k = cosh + sinhi, as hyperbolic-isoclinic rotations in R3,1.