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arXiv · 1302.5926

Maximal abelian subalgebras of the group factor of an $\widetilde A_2$ group

Guyan Robertson·Tim Steger
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Abstract

An $\widetilde A_2$ group $Γ$ acts simply transitively on the vertices of an affine building $\triangle$. We study certain subgroups $Γ_0 \cong {\Bbb Z}^2$ which act on certain apartments of $\triangle$. If one of these subgroups acts simply transitively on an apartment, then the corresponding subalgebra of the group von Neumann algebra is maximal abelian and singular. Moreover the Pukánszky invariant contains a type $I_{\infty}$ summand.

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Guyan Robertson, Tim Steger. 2013-02-24. Maximal abelian subalgebras of the group factor of an $\widetilde A_2$ group. https://arxiv.org/abs/1302.5926

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