The Pukánszky invariant for masas in group von Neumann factors
Sinclair, Allan M. ; Smith, Roger R.
Illinois J. Math., Tome 49 (2005) no. 2, p. 325-343 / Harvested from Project Euclid
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The Pukánszky invariant associates to each maximal abelian self-adjoint subalgebra (masa) $A$ in a type $\operatorname{II}_1$ factor $M$ a certain subset ot $\mathbb N\cup\{\infty\}$, denoted by $\operatorname{Puk}(A)$. We study this invariant in the context of factors generated by infinite conjugacy class discrete countable groups $G$ with masas arising from abelian subgroups $H$. Our main result is that we are able to describe $\operatorname{Puk}(VN(H))$ in terms of the algebraic structure of $H\subseteq G$, specifically by examining the double cosets of $H$ in $G$. We illustrate our characterization by generating many new values for the invariant, mainly for masas in the hyperfinite type $\operatorname{II}_1$ factor $R$.
Publié le : 2005-04-15
Classification:  46L10,  22D25 
@article{1258138021,
     author = {Sinclair, Allan M. and Smith, Roger R.},
     title = {The Puk\'anszky invariant for masas in group von Neumann factors},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 325-343},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138021}
}

Sinclair, Allan M.; Smith, Roger R. The Pukánszky invariant for masas in group von Neumann factors. Illinois J. Math., Tome 49 (2005) no. 2, pp.  325-343. http://gdmltest.u-ga.fr/item/1258138021/