Splitting fields of mixed Cayley graphs over abelian groups

The splitting field SF(Gamma) of a mixed graph Gamma is the smallest field extension of Q which contains all eigenvalues of the Hermitian adjacency matrix of Gamma. The extension degree [SF(Gamma) : Q] is called the algebraic degree of Gamma. In this paper, we determine the splitting fields and algebraic degrees of mixed Cayley graphs over abelian groups. This generalizes the main results of Monius (J Algebra 594(15):154-169, 2022). Additionally, we provide a characterization of integralmixed Cayley graphs over abelian groups, which implies the main result of Kadyan and Bhattacharjya (Electron J Combin 28(4):P4.46, 2021).