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The splitting field $\mathbb{SF}(\Gamma)$ of a mixed graph $\Gamma$ is thesmallest field extension of $\mathbb{Q}$ which contains all eigenvalues of theHermitian adjacency matrix of $\Gamma$. The extension degree$[\mathbb{SF}(\Gamma):\mathbb{Q}]$ is called the algebraic degree of $\Gamma$.In this paper, we determine the splitting fields and algebraic degrees of mixedCayley graphs over abelian groups. This generalizes the main results of [K.M\"{o}nius, Splitting fields of spectra of circulant graphs, J. Algebra 594(15)(2022) 154--169] and [M. Kadyan, B. Bhattacharjya, Integral mixed Cayley graphsover abelian groups, Electron. J. Combin. 28(4) (2021) \#P4.46].

Splitting fields of mixed Cayley graphs over abelian groups