An Invitation to Split Quaternionic Analysis

Details An Invitation to Split Quaternionic Analysis An Invitation to Split Quaternionic Analysis

2010-09-13

arxiv.org/abs/1009.2540v1

Mathematics

Complex Variables

18 pages, 1 figure, accepted for publication

Scientific paper

Six years after William Rowan Hamilton's discovery of quaternions, in 1849 James Cockle introduced the algebra of split quaternions. (He called them ``coquaternions.'') In this paper we define regular functions on split quaternions and prove two different analogues of the Cauchy-Fueter formula for these functions. In the paper "Split quaternionic analysis and the separation of the series for SL(2,R) and SL(2,C)/SL(2,R)" joint with Igor Frenkel we naturally apply the methods and formulas of quaternionic analysis to solve the problems of harmonic analysis on SL(2,R) and the imaginary Lobachevski space SL(2,C)/SL(2,R).

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