Graded Lie-Cartan pairs. I (Q1109867)

The Lie-Cartan pairs were defined in a previous paper of \textit{D. Kastler} and \textit{R. Stora} [J. Geom. Phys. 2, No. 3, 1--31 (1985; Zbl 0593.17009)] where \(L\) was a Lie algebra and \(A\) was a commutative (associative) algebra. In this paper a generalization of such pairs \((L,A)\) is given for a Lie superalgebra \(L\) and graded commutative algebra \(A\). The classical operators attached to \((L,A)\) are defined and their properties are studied in Sections 2 and 4. Section 3 describes tensoring by graded commutative algebras and the corresponding connections on the tensor-pairs. Appendix A is a summary of graded vector spaces and superalgebras, and Appendix B describes ``graded symmetrization''.