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3-Parameter Generalized Quaternions

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dc.contributor.authorTuncay Deniz, Şentürk
dc.contributor.authorZafer, Ünal
dc.date.accessioned2026-01-04T16:49:38Z
dc.date.issued2022-05-25
dc.description.abstractIn this article, we give the most genaral form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study on various properties and applications. Firstly we present the definiton, the multiplication table another properties of 3PGQs such as addition-substraction, multiplication and multiplication by scalar operations, unit and inverse elements, conjugate and norm. We give matrix representation and Hamilton operators for 3PGQs. We get polar represenation, De Moivre's and Euler's formulas with the matrix representations for 3PGQs. Besides, we give relations among the powers of the matrices associated with 3PGQs. Finally, Lie group and Lie algebra are studied and their matrix representations are shown. Also the Lie multiplication and the killing bilinear form are given.
dc.description.abstract30 pages
dc.description.urihttps://doi.org/10.1007/s40315-022-00451-7
dc.description.urihttps://dx.doi.org/10.48550/arxiv.2101.11928
dc.description.urihttp://arxiv.org/abs/2101.11928
dc.description.urihttps://zbmath.org/7581354
dc.identifier.doi10.1007/s40315-022-00451-7
dc.identifier.eissn2195-3724
dc.identifier.endpage608
dc.identifier.issn1617-9447
dc.identifier.openairedoi_dedup___::ae8a4ffb097a75f108010f60b97eb6f9
dc.identifier.orcid0000-0002-5247-5097
dc.identifier.scopus2-s2.0-85130743426
dc.identifier.startpage575
dc.identifier.urihttps://hdl.handle.net/20.500.12597/39705
dc.identifier.volume22
dc.identifier.wos000801839400001
dc.language.isoeng
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofComputational Methods and Function Theory
dc.rightsOPEN
dc.subjectClifford algebras, spinors
dc.subjectA20, 14A22, 15A66, 70G55, 70G65
dc.subjectMathematics - Algebraic Geometry
dc.subjectMatrices over special rings (quaternions, finite fields, etc.)
dc.subjectparameter generalized quaternion
dc.subjectLie algebra
dc.subjectEuler formula
dc.subjectde Moivre formula
dc.subjectFOS: Mathematics
dc.subjectQuaternion and other division algebras: arithmetic, zeta functions
dc.subjectmatrix representation of quaternions
dc.subjectAlgebraic Geometry (math.AG)
dc.title3-Parameter Generalized Quaternions
dc.typeArticle
dspace.entity.typePublication
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