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- W4226154666 abstract "By analogy with the construction of the Furstenberg boundary, the Stone-{v C}ech boundary of $SL(3,mathbb{Z})$ is a fibered space over products of projective matrices. The proximal behaviour on this space is exploited to show that the preimages of certain sequences have accumulation points which belong to specific regions, defined in terms of flags. We show that the $SL(3,mathbb{Z})times SL(3,mathbb{Z})$-quasi-invariant Radon measures supported on these regions are tempered. Thus every quasi-invariant Radon boundary measure for $SL(3,mathbb{Z})$ is an orthogonal sum of a tempered measure and a measure having matrix coefficients belonging to a certain ideal $c'_0 ((SL(3,mathbb{Z}) times SL(3,mathbb{Z}))$, slightly larger than $c_0 ((SL(3,mathbb{Z}) times SL(3,mathbb{Z}))$. Hence the left-right representation of $C^*(SL(3,mathbb{Z}) times SL(3,mathbb{Z}))$ in the Calkin algebra of $SL(3,mathbb{Z})$ factors through $C^*_{c'_0} (SL(3,mathbb{Z}) times SL(3,mathbb{Z}))$ and the centralizer of every infinite subgroup of $SL(3,mathbb{Z})$ is amenable." @default.
- W4226154666 created "2022-05-05" @default.
- W4226154666 creator A5040283645 @default.
- W4226154666 creator A5064036516 @default.
- W4226154666 date "2021-11-27" @default.
- W4226154666 modified "2023-09-29" @default.
- W4226154666 title "A mixing property for the action of $SL(3,mathbb{Z})timesSL(3,mathbb{Z})$ on the Stone-Cech boundary of $SL(3,mathbb{Z})$" @default.
- W4226154666 doi "https://doi.org/10.48550/arxiv.2111.13885" @default.
- W4226154666 hasPublicationYear "2021" @default.
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