A representation of the coalgebra of derivations for smooth spaces

Fischer, Gerald

Proceedings of the 18th Winter School "Geometry and Physics", GDML_Books, (1999), p. 135-141 / Harvested from

Résumé

Let $K$ be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra $𝒟_{K}^{k}$ for any positive integer $k$ . This is spanned over $K$ by $d_{0}, ..., d_{k}$ , and has comultiplication $Δ$ and counit $ε$ defined by $Δ (d_{i}) = \sum_{j = 0}^{i} d_{j} \otimes d_{i - j}$ and $ε (d_{i}) = δ_{0, i}$ (Kronecker’s delta) for any $i$ . This note presents a representation of the coalgebra $𝒟_{K}^{k}$ by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.

MR MR1692264 | Zbl 0962.16027

EUDML-ID : urn:eudml:doc:221879
Mots clés:

@article{701632,
     title = {A representation of the coalgebra of derivations for smooth spaces},
     booktitle = {Proceedings of the 18th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1999},
     pages = {135-141},
     mrnumber = {MR1692264},
     zbl = {0962.16027},
     url = {http://dml.mathdoc.fr/item/701632}
}

Fischer, Gerald. A representation of the coalgebra of derivations for smooth spaces, dans Proceedings of the 18th Winter School "Geometry and Physics", GDML_Books,  (1999), pp. 135-141. http://gdmltest.u-ga.fr/item/701632/