Split Semi-quaternions Algebra in Semi-Euclidean 4-Space

Yıl 2015, Cilt: 36 Sayı: 1, 70 - 77, 01.03.2015

Mehdi Jafarı

Öz

The aim of this paper is to study the split semi-quaternions,

Hss;and to give some of their algebra properties. We show that the set of unit split semi-quaternions is a subgroup ofHss: Furthermore, with the aid of De Moivre.s formula, any powers of these quaternions can be obtained.

 

 

Anahtar Kelimeler

De Moivre’s formula, Split semi-quaternion, Euler’s formula

SPLIT SEMI-QUATERNIONS ALGEBRA IN SEMI-EUCLIDEAN 4-SPACE

Öz

Abstract.

The aim of this paper is to study the split semi-quaternions,

Hss;and to give some of their algebraic properties. We show that the set of unitsplit semi-quaternions is a subgroup of

Hss:Furthermore, with the aid of De

Moivre's formula, any powers of these quaternions can be obtaine

Anahtar Kelimeler

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Kaynakça

• Brand L.. The roots of a Quaternion, American Mathematical Monthly 49-8(1942) 519-520.
• Mortezaasl H., Jafari M., A study on Semi-quaternions Algebra in Semi-Euclidean 4-space, Mathematical Science and Applications E-Notes, Vol. 1/2,(2013) 20-27.
• Niven I. The roots of a quaternion, American Mathematical Monthly 49-6(1942) 386-388.
• Ozdemir M., The roots of a split quaternion, Appl. Math. Lett. 22(2009) 258-263.
• Rosenfeld B., Geometry of Lie groups, Kluwer Academic Publishers, Netherlands,1997.