Abstract We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first-order evolution equations defined on T¹ G T 1 × G, where G is a compact Lie group. First, we show that the global hypoellipticity of the constant coefficient operator related to this operator is a necessary condition, but not a sufficient condition. Under certain hypothesis, we show that the global hypoellipticity of this class of operator is completely characterized by Nirenberg–Treves’ condition (P) (P).
Wagner Augusto Almeida de Moraes (Mon,) studied this question.