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2008-09-07 22:10:44
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bci1
\begin{remark}
A \emph{groupoid C*-dynamical system} can be regarded as an extension of the ordinary concept
of dynamical system. Thus, it can also be utilized to represent a quantum dynamical system
upon further specification of the C*-algebra as a von Neumann algebra, and also of $\grp_{lc}$
as a quantum groupoid; in the latter case, with additional conditions it can also simulate either quantum automata,
or variable classical automata, depending on the added restrictions (ergodicity, etc.).
\end{remark} |
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2008-09-07 21:52:49
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bci1
46L55 (Functional analysis :: Selfadjoint operator algebras :: Noncommutative dynamical systems)
55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory)
37B45 (Dynamical systems and ergodic theory :: Topological dynamics :: Continua theory in dynamics)
18B30 (Category theory; homological algebra :: Special categories :: Categories of topological spaces and continuous mappings)
22A22 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Topological groupoids )
22D25 (Topological groups, Lie groups :: Locally compact groups and their algebras :: $C^*$-algebras and $W$*-algebras in relation to group representations)
55P10 (Algebraic topology :: Homotopy theory :: Homotopy equivalences)
55N20 (Algebraic topology :: Homology and cohomology theories :: Generalized homology and cohomology theories)
55U99 (Algebraic topology :: Applied homological algebra and category theory :: Miscellaneous)
55N33 (Algebraic topology :: Homology and cohomology theories :: Intersection homology and cohomology)
18D05 (Category theory; homological algebra :: Categories with structure :: Double categories, $2$-categories, bicategories and generalizations \\\
msc:22A22,28C10,22D25, 46L55, msc:37B45, 18D05, msc:18B30, 46L85 msc:55U40, msc:55P10, msc:55N20, msc:55N33 |
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2008-09-07 21:39:39
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bci1
| msc:46L55, msc:55U40, 37B45, 18B30, 22A22, 22D25, msc:55P10, msc:55N20, 55U99, msc:55N33, msc:18D05 |
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2008-08-23 17:11:53
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Version 9 --> Version 10
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bci1
(Definition introduced in ref. \cite{MT1984}.)
\end{definition}
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