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Martin Sleziak
Martin Sleziak
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No, if $\Gamma$ is a group without torsion and with the Infinite conjugacy class property then the algebra $L\Gamma$ is a factor of type $II$ and has only one normal tracial state.

Now, let $x $ in $\Gamma$ different from the identity. The vonNeumannvon Neumann algebra $S$ generated by $x$ is isomorphic to $L^\infty(S^1)$, the algebra of measurable functions on the circle. It has many normal tracial states.

No, if $\Gamma$ is a group without torsion and with the Infinite conjugacy class property then the algebra $L\Gamma$ is a factor of type $II$ and has only one normal tracial state.

Now, let $x $ in $\Gamma$ different from the identity. The vonNeumann algebra $S$ generated by $x$ is isomorphic to $L^\infty(S^1)$, the algebra of measurable functions on the circle. It has many normal tracial states.

No, if $\Gamma$ is a group without torsion and with the Infinite conjugacy class property then the algebra $L\Gamma$ is a factor of type $II$ and has only one normal tracial state.

Now, let $x $ in $\Gamma$ different from the identity. The von Neumann algebra $S$ generated by $x$ is isomorphic to $L^\infty(S^1)$, the algebra of measurable functions on the circle. It has many normal tracial states.

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InfiniteLooper
InfiniteLooper
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No, if $\Gamma$ is a group without torsion and with the Infinite conjugacy class property then the algebra $L\Gamma$ is a factor of type $II$ and has only one normal tracial state.

Now, let $x $ in $\Gamma$ different from the identity. The vonNeumann algebra $S$ generated by $x$ is isomorphic to $L^\infty(S^1)$, the algebra of measurable functions on the circle. It has many normal tracial states.