GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES

Jafari, Mehdi; YAYLI, YUSUF

doi:10.1501/commua1_0000000724

GENERALIZED QUATERNIONS AND THEIR ALGEBRAIC PROPERTIES

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.64, sa.1, ss.15-27, 2015 (ESCI)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 64 Sayı: 1
Basım Tarihi: 2015
Doi Numarası: 10.1501/commua1_0000000724
Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.15-27
Anahtar Kelimeler: De-Moivre's formula, Generalized quaternion, Lie group
Ankara Üniversitesi Adresli: Evet

Özet

The aim of this paper is to study the generalized quaternions, H-alpha beta, and their basic properties. H-alpha beta has a generalized inner product that allows us to identify it with four-dimensional space E-alpha beta(4). Also, it is shown that the set of all unit generalized quaternions with the group operation of quaternion multiplication is a Lie group of 3-dimension and its Lie algebra is found.