A New Polar Representation for Split and Dual Split Quaternions

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dc.contributor.authorAtasoy, Ali
dc.contributor.authorAta, Erhan
dc.contributor.authorYayli, Yusuf
dc.contributor.authorKemer, Yasemin
dc.date.accessioned2020-06-25T18:22:47Z
dc.date.available2020-06-25T18:22:47Z
dc.date.issued2017
dc.departmentKırıkkale Üniversitesi
dc.description.abstractWe present a new different polar representation of split and dual split quaternions inspired by the Cayley-Dickson representation. In this new polar form representation, a split quaternion is represented by a pair of complex numbers, and a dual split quaternion is represented by a pair of dual complex numbers as in the Cayley-Dickson form. Here, in a split quaternion these two complex numbers are a complex modulus and a complex argument while in a dual split quaternion two dual complex numbers are a dual complex modulus and a dual complex argument. The modulus and argument are calculated from an arbitrary split quaternion in Cayley-Dickson form. Also, the dual modulus and dual argument are calculated from an arbitrary dual split quaternion in Cayley-Dickson form. By the help of polar representation for a dual split quaternion, we show that a Lorentzian screw operator can be written as product of two Lorentzian screw operators. One of these operators is in the two-dimensional space produced by 1 and i vectors. The other is in the three-dimensional space generated by 1, j and k vectors. Thus, an operator in a four-dimensional space is expressed by means of two operators in two and three-dimensional spaces. Here, vector 1 is in the intersection of these spaces.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1007/s00006-017-0797-8
dc.identifier.endpage2319en_US
dc.identifier.issn0188-7009
dc.identifier.issn1661-4909
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85021783122
dc.identifier.scopusqualityQ3
dc.identifier.startpage2307en_US
dc.identifier.urihttps://doi.org/10.1007/s00006-017-0797-8
dc.identifier.urihttps://hdl.handle.net/20.500.12587/6902
dc.identifier.volume27en_US
dc.identifier.wosWOS:000408268200021
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Basel Agen_US
dc.relation.ispartofAdvances In Applied Clifford Algebras
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectDual split quaternionen_US
dc.subjectPolar formen_US
dc.subjectSplit quaternionen_US
dc.subjectScrew operatoren_US
dc.titleA New Polar Representation for Split and Dual Split Quaternionsen_US
dc.typeArticle

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