Krein space features of the MHD alpha² - dynamo operator matrix

The spherical MHD mean-field dynamo is considered from a mathematical viewpoint. It is shown that its 2x2 operator matrix is formally pseudo-Hermitian (J-symmetric), lives in a Krein space and has paired complex eigenvalues. Based on the J-symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the alpha²-dynamo operator matrix. An intrinsic structural inconsistency is obtained in the set of associated matrix Riccati equations. This inconsistency is interpreted as a no-go theorem which forbids the construction of isospectral alpha²-dynamo operator classes with the help of first-order differential intertwining operators.