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Poincaré Lemma on Quaternion-like Heisenberg Groups
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2018