Gradings on the simple real Lie algebras of types \(G_2\) and \(D_4\) (Q1655813)

In a series of papers Yu. Bahturin, A. Rodrigo-Escudero, A. J. Calderón Martín, C. Draper, C. Martín González and the authors in 2010--2020 published a series of papers of various kinds of group gradings in simple known algebras. One can find a presentation of all gradings in the case of algebraically closed field of characteristic zero in the authors' book [Gradings on simple Lie algebras. Providence, RI: American Mathematical Society (AMS) (2013; Zbl 1281.17001)]. In the present paper the remaining cases of simple Lie algebras of types \(G_2\) and \(D_4\) are considered under the assumption that the basic field is real closed. A classification is given up to an equivalence. A particular case of fine gradings is considered in detail.