# A representation of the coalgebra of derivations for smooth spaces

- Proceedings of the 18th Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page 135-141

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topFischer, Gerald. "A representation of the coalgebra of derivations for smooth spaces." Proceedings of the 18th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1999. 135-141. <http://eudml.org/doc/221879>.

@inProceedings{Fischer1999,

abstract = {Let $K$ be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra $\{\mathcal \{D\}\}^k_K$ for any positive integer $k$. This is spanned over $K$ by $d_0,\ldots ,d_k$, and has comultiplication $\Delta $ and counit $\varepsilon $ defined by $\Delta (d_i)=\sum _\{j=0\}^id_j\otimes d_\{i-j\}$ and $\varepsilon (d_i)=\delta _\{0,i\}$ (Kronecker’s delta) for any $i$. This note presents a representation of the coalgebra $\{\mathcal \{D\}\}^k_K$ 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.},

author = {Fischer, Gerald},

booktitle = {Proceedings of the 18th Winter School "Geometry and Physics"},

keywords = {Winter school; Proceedings; Geometry; Physics; Srní (Czech Republic)},

location = {Palermo},

pages = {135-141},

publisher = {Circolo Matematico di Palermo},

title = {A representation of the coalgebra of derivations for smooth spaces},

url = {http://eudml.org/doc/221879},

year = {1999},

}

TY - CLSWK

AU - Fischer, Gerald

TI - A representation of the coalgebra of derivations for smooth spaces

T2 - Proceedings of the 18th Winter School "Geometry and Physics"

PY - 1999

CY - Palermo

PB - Circolo Matematico di Palermo

SP - 135

EP - 141

AB - Let $K$ be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra ${\mathcal {D}}^k_K$ for any positive integer $k$. This is spanned over $K$ by $d_0,\ldots ,d_k$, and has comultiplication $\Delta $ and counit $\varepsilon $ defined by $\Delta (d_i)=\sum _{j=0}^id_j\otimes d_{i-j}$ and $\varepsilon (d_i)=\delta _{0,i}$ (Kronecker’s delta) for any $i$. This note presents a representation of the coalgebra ${\mathcal {D}}^k_K$ 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.

KW - Winter school; Proceedings; Geometry; Physics; Srní (Czech Republic)

UR - http://eudml.org/doc/221879

ER -

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