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Summer 2005 The Pukánszky invariant for masas in group von Neumann factors
Allan M. Sinclair, Roger R. Smith
Illinois J. Math. 49(2): 325-343 (Summer 2005). DOI: 10.1215/ijm/1258138021

Abstract

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 $R$.

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Allan M. Sinclair. Roger R. Smith. "The Pukánszky invariant for masas in group von Neumann factors." Illinois J. Math. 49 (2) 325 - 343, Summer 2005. https://doi.org/10.1215/ijm/1258138021

Information

Published: Summer 2005
First available in Project Euclid: 13 November 2009

zbMATH: 1092.46045
MathSciNet: MR2163938
Digital Object Identifier: 10.1215/ijm/1258138021

Subjects:
Primary: 46L10
Secondary: 22D25

Rights: Copyright © 2005 University of Illinois at Urbana-Champaign

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Vol.49 • No. 2 • Summer 2005
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