Clifford analysis versus its quaternionic counterparts

✍ Scribed by Juan Bory Reyes; Michael Shapiro

• Book ID: 102510419
• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 237 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1238

✦ Synopsis

Communicated by K. Gürlebeck

For a positive integer n let Cl 0,n be the universal Clifford algebra with the signature (0,n). The name Clifford analysis is usually referred to the function theories for functions in the kernels of the two operators: the (Cliffordian) Cauchy-Riemann operator and the Dirac operator. For n = 2, Cl 0,2 becomes the skew-field of Hamilton's quaternions for which the two operators are widely known: the Moisil-Théodoresco and the Fueter operators. We establish the precise relations between the Moisil-Théodoresco operator and the Dirac operator for Cl 0,3 . It turns out that the case of the Cauchy-Riemann operator for Cl 0,3 and the Fueter operator is more sophisticated, and we describe the peculiarities emerging here.