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Let $M$ be a type $II_{1}$ factor, Let $B$ is an infinite dimensional nonabelian subalgebra. Is it true that $B$ always type $II_{1}$ too?

Let $M$ be a type $II_{1}$ factor, Let $B$ is an infinite dimensional nonabelian subalgebra. Is it true that $B$ type $II_{1}$ too?

Let $M$ be a type $II_{1}$ factor, Let $B$ is an infinite dimensional nonabelian subalgebra. Is it true that $B$ always type $II_{1}$ ?

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user136400
  • 677
  • 3
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Subalgebras of $II_{1}$ factor

Let $M$ be a type $II_{1}$ factor, Let $B$ is an infinite dimensional nonabelian subalgebra. Is it true that $B$ type $II_{1}$ too?