Die Cartan-Algebra der äusseren Differentialformen als Supermannigfaltigkeit: Automorphismen, Jordan-Automorphismen und ihre Realisierung als Diffeomorphismen

Abstract

In the Cartan algebra we constructively enumerate all automorphisms, all splitting and function subalgebras, and a class of Jordan automorphisms. We show representability of the automorphisms resp. Jordan automorphisms as diffeomorphisms on a fibred space over the given manifold $M$. Its dimensionality is 15 resp. 24 if dim $M$ = 3, and 32 resp. 64 if dim $M$ = 4.