| Version 10 |
Version 9 |
| \begin{definition} |
\begin{definition} |
| A \emph{C*-groupoid system} or \emph{groupoid C*-dynamical system} |
A \emph{C*-groupoid system} or \emph{groupoid C*-dynamical system} |
| is a \emph{triple} $(A, \grp_{lc}, \rho )$, where: |
is a \emph{triple} $(A, \grp_{lc}, \rho )$, where: |
| $A$ is a C*-algebra, and $\grp_{lc}$ is a locally compact (topological) groupoid |
$A$ is a C*-algebra, and $\grp_{lc}$ is a locally compact (topological) groupoid |
| with a countable basis for which there exists an associated continuous Haar system and a continuous |
with a countable basis for which there exists an associated continuous Haar system and a continuous |
| groupoid (homo) morphism $\rho: \grp_{lc} \longrightarrow Aut(A)$ defined |
groupoid (homo) morphism $\rho: \grp_{lc} \longrightarrow Aut(A)$ defined |
| by the assignment $x \mapsto \rho_x(a)$ (from $\grp_{lc}$ to $A$) |
by the assignment $x \mapsto \rho_x(a)$ (from $\grp_{lc}$ to $A$) |
| which is continuous for any $a \in A$; moreover, one considers the norm topology |
which is continuous for any $a \in A$; moreover, one considers the norm topology |
| on $A$ in defining $\grp_{lc}$. (Definition introduced in ref. \cite{MT1984}.) |
on $A$ in defining $\grp_{lc}$. (Definition introduced by Matsuda (1984), |
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\cite{MT1984}, also cited in Buneci (2003)). |
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| \end{definition} |
\end{definition} |
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| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{MT1984} |
\bibitem{MT1984} |
| T. Matsuda, Groupoid dynamical systems and crossed product, II-case of C*-systems., |
T. Matsuda, Groupoid dynamical systems and crossed product, II-case of C*-systems., |
| \emph{Publ. RIMS}, Kyoto Univ., \textbf{20}: 959-976 (1984). |
\emph{Publ. RIMS}, Kyoto Univ., \textbf{20}: 959-976 (1984). |
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| \end{thebibliography} |
\end{thebibliography} |
