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Article overview
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Primeness results for von Neumann algebras associated with surface braid groups | | Ionut Chifan
; Yoshikata Kida
; Sujan Pant
; | | Date: |
27 Dec 2014 | | Abstract: | In this paper we introduce a new class $mathcal{P}$ of non-amenable groups
which give rise to prime von Neumann algebras. This means that for every
$Gamma in mathcal{P}$ its group von Neumann algebra $L(Gamma)$ cannot be
decomposed as a tensor product of diffuse von Neumann algebras. We show that
$mathcal{P}$ is fairly large as it contains many examples of groups
intensively studied in various areas of mathematics, notably: all infinite
central quotients of pure surface braid groups---in particular, most pure braid
groups on punctured surfaces of genus at least $1$; all mapping class groups of
(punctured) surfaces of genus $0,1,2$; most Torelli groups and Johnson kernels
of (punctured) surfaces of genus $0,1,2$; and, all groups hyperbolic relative
to finite families of residually finite, exact, infinite, proper subgroups. | | Source: | arXiv, 1412.8025 | | Services: | Forum | Review | PDF | Favorites | |
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