比利时vs摩洛哥足彩
,
university of california san diego
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math 243 - seminar in operator algebras
daniel hoff
ucla
unique factorization of ${\rm ii}_1$ factors of groups measure equivalent to products of hyperbolic groups
abstract:
a ${\rm ii}_1$ factor $m$ is called prime if it cannot be decomposed as a tensor product of ${\rm ii}_1$ subfactors. naturally, if $m$ is not prime, one asks if $m$ can be uniquely factored as a tensor product of prime subfactors. the first result in this direction is due to ozawa and popa in 2003, who gave a large class of groups $\mathcal{c}$ such that for any $\gamma_1, \dots, \gamma_n \in \mathcal{c}$, the associated von neumann algebra $l(\gamma_1) \,\overline{\otimes}\, \cdots \,\overline{\otimes}\, l(\gamma_n)$ is uniquely factored in a strong sense. this talk will consider the case where $\gamma$ is icc group that is measure equivalent to a product of non-elementary hyperbolic groups. in joint work with daniel drimbe and adrian ioana, we show that any such $\gamma$ admits a unique decomposition $\gamma = \gamma_1 \times \gamma_2 \times \cdots \times \gamma_n$ such that $l(\gamma) = l(\gamma_1) \,\overline{\otimes}\, \cdots \,\overline{\otimes}\, l(\gamma_n)$ is uniquely factored in sense of ozawa and popa. using this, we provide the first examples of prime ${\rm ii}_1$ factors arising from lattices in higher rank lie groups.
host: adrian ioana
january 31, 2017
2:00 pm
ap&m 7321
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