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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 01/2003

α. ν. χεςϋιλ
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στςαξξωε ζαλτος-πςεδσταχμεξιρ τιπα $\amalg_1$ ι
παςω δυαμψξωθ διξανιώεσλιθ σιστεν

This preprint was accepted January 4, 2003

Contact:
` α. ν.χεςϋιλ `

ABSTRACT:
We describe a construction of the factor-representations of type
$\amalg_1$ corresponding to some {\it pair of the dynamical systems}.
This is a generalization of the classical von Neumann
construction of the factors as the crossed-product and of the grouppoid
approach. We present the natural examples of factor-representations
of this type for which so called {\it coupling constant could
be not equal to one} and consequently there are no spatial
traces. The simplest example of such situation gives a pair
of discrete subgroups of Heisenberg group (see \cite{F}), which provide
also the new kind of factor-representations of type $\amalg_1$ of rotation algebra.
Another examples come from the theory of the lattices in the groups and
from the theory of representations of infinite symmetric group.

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