Generalized Lie-Cartan pairs
\textit{D. Kastler} and \textit{R. Stora} [J. Geom. Phys. 2, No. 3, 1-31 (1985; Zbl 0593.17009)] defined the Lie-Cartan pairs \((L,A)\) of a Lie algebra \(L\) and a commutative algebra \(A\). \textit{A. Jadczyk} and \textit{D. Kastler} [Rep. Math. Phys. 25, No. 1, 1-51 (1988; Zbl 0656.17014)] generalized the concept of Lie-Cartan pairs to the \(\mathbb{Z}_ 2\)-graded case. The author generalizes it to the \(\Gamma\)-graded case, where \(\Gamma\) is a \(p\)-group for \(p=2\). The author shows that classical operators of differential geometry such as the exterior derivative, covariant derivative, the inner product, Lie derivative can be extended to the \(\Gamma\)-graded case.
scientific article; zbMATH DE number 21546