An introduction to commutative quaternions

Francesco Catoni, Roberto Cannata, Paolo Zampetti

Research output: Contribution to journalArticle

27 Citations (Scopus)


A Scheffers theorem states that for commutative hypercomplex numbers the differential calculus does exist and the functions can be introduced in the same way as they are for the complex variable. This property could open new applications of commutative quaternions in comparison with non-commutative Hamilton quaternions. In this article we introduce some quaternionic systems, their algebraic properties and the differential conditions (Generalized Cauchy-Riemann conditions) that their functions must satisfy. Then we show that the functional mapping, studied in the geometry associated with the quaternions, does have the same properties of the conformal mapping performed by the functions of complex variable. We also summarize the expressions of the elementary functions. © 2006 Birkhäuser Verlag, Basel.
Original languageEnglish
Pages (from-to)1 - 28
Number of pages28
JournalAdvances in Applied Clifford Algebras
Issue number1
Publication statusPublished - Feb 2006
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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