We review the basic facts about the theory of paracommutators in Rn (sec S. Janson, J. Peetre, Trans. Am. Math. Soc. 305 (1988), 467504). We also give an interpretation of paracommutators from the point of view of group representations. This suggests a generalization to more general groups. Here we sketch a theory of paracommutators over stratified groups. This include the famous Heisenberg group. Finally, we take up the question of generalizing the notion of Schatten-von Neumann trace ideals to the case of multilinear forms in (abstract) Hilbert spaces.
@article{urn:eudml:doc:43487,
title = {Paracommutators. Brief introduction, open problems.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {2},
year = {1989},
pages = {201-211},
zbl = {0726.47022},
mrnumber = {MR1057219},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43487}
}
Peetre, Jaak. Paracommutators. Brief introduction, open problems.. Revista Matemática de la Universidad Complutense de Madrid, Tome 2 (1989) pp. 201-211. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43487/