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N-dimensional geometries generated by hypercomplex numbers

TitoloN-dimensional geometries generated by hypercomplex numbers
Tipo di pubblicazioneArticolo su Rivista peer-reviewed
Anno di Pubblicazione2005
AutoriCatoni, F., Cannata R., Catoni V., and Zampetti P.
RivistaAdvances in Applied Clifford Algebras
Volume15
Paginazione1-25
ISSN01887009
Abstract

The geometries in N-dimensional Euclidean spaces can be described by Clifford algebras that were introduced as extensions of complex numbers. These applications are due to the fact that the Euclidean invariant (the distance between two points) is the same as the one of Clifford numbers. In this paper we consider the more general extension of complex numbers due to their group properties (hypercomplex systems), and we introduce the N-dimensional geometries associated with these systems. For N > 2 these geometries are different from the N-dimensional Euclidean geometries; then their investigation could open new applications. Moreover for the commutative systems the differential calculus does exist and this property allows one to define the functions of hypercomplex variable that can be used for studying some partial differential equations as well as the non-flat N-dimensional spaces. This last property can be relevant in general relativity and in field theories. © 2005 Birkhäuser Verlag, Basel.

Note

cited By 14

URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-20444413961&doi=10.1007%2fs00006-005-0001-4&partnerID=40&md5=7dce6d9a7d2b5903c3a2eb0735f6a1d2
DOI10.1007/s00006-005-0001-4
Citation KeyCatoni20051