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Poincaré Lemma on Quaternion-like Heisenberg Groups

Published online by Cambridge University Press:  20 November 2018

Der-Chen Chang ,
Nanping Yang  and
Hsi-Chun Wu
Der-Chen Chang
Affiliation:
Department of Mathematics and Statistics, Georgetown University, Washington D.C. 20057, USA, e-mail : chang@georgetown.edu Department of Mathematics, Fu Jen Catholic University, Taipei 242, Taiwan, ROC, e-mail : yang@math.fju.edu.tw
Nanping Yang
Affiliation:
Department of Mathematics and Statistics, Georgetown University, Washington D.C. 20057, USA, e-mail : chang@georgetown.edu Department of Mathematics, Fu Jen Catholic University, Taipei 242, Taiwan, ROC, e-mail : yang@math.fju.edu.tw
Hsi-Chun Wu
Affiliation:
Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, Taipei 242, Taiwan, ROC, e-mail : 400068060@mail.fju.edu.tw
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Abstract

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For smooth functions ${{a}_{1}}\,,\,{{a}_{2}}\,,\,{{a}_{3}}\,,\,{{a}_{4}}\,$ on a quaternion Heisenberg group, we characterize the existence of solutions of the partial differential operator system ${{X}_{1}}f\,=\,{{a}_{1}},\,{{X}_{2}}f=\,{{a}_{2}},\,{{X}_{3}}f\,=\,{{a}_{3}},\,\text{and}\,{{X}_{4}}f\,=\,{{a}_{4}}$. In addition, a formula for the solution function $f$ is deduced, assuming solvability of the system.

Keywords

93B0549N99bracket generating propertyquaternion Heisenberg groupcurlintegrability conditionPoincaré lemma
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 3 , 01 September 2018 , pp. 495 - 508
Copyright
Copyright © Canadian Mathematical Society 2018

References

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