Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

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dc.contributor.authorStodola, Marekcs
dc.contributor.authorHrdina, Jaroslavcs
dc.coverage.issue4cs
dc.coverage.volume34cs
dc.date.issued2024-08-31cs
dc.description.abstractUsing the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).en
dc.description.abstractUsing the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).en
dc.formattextcs
dc.format.extent1-22cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Applied Clifford Algebras. 2024, vol. 34, issue 4, p. 1-22.en
dc.identifier.doi10.1007/s00006-024-01346-7cs
dc.identifier.issn0188-7009cs
dc.identifier.orcid0000-0003-2460-7571cs
dc.identifier.other189563cs
dc.identifier.researcheridK-7147-2019cs
dc.identifier.scopus14044864000cs
dc.identifier.urihttp://hdl.handle.net/11012/250095
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofAdvances in Applied Clifford Algebrascs
dc.relation.urihttps://link.springer.com/article/10.1007/s00006-024-01346-7cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0188-7009/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectConicsen
dc.subjectGeometric algebraen
dc.subjectPGAen
dc.subjectCGAen
dc.subjectGACen
dc.subjectWitt pairsen
dc.subjectPythonen
dc.subjectConics
dc.subjectGeometric algebra
dc.subjectPGA
dc.subjectCGA
dc.subjectGAC
dc.subjectWitt pairs
dc.subjectPython
dc.titleHigher Order Geometric Algebras and Their Implementations Using Bott Periodicityen
dc.title.alternativeHigher Order Geometric Algebras and Their Implementations Using Bott Periodicityen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-189563en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 15:06:59en
sync.item.modts2025.10.14 10:11:45en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs

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