TITLE

Von Neumann algebras associated with the group SL(ℝ)

AUTHOR(S)
Wu, Wen
PUB. DATE
September 2011
SOURCE
Acta Mathematica Sinica;Sep2011, Vol. 27 Issue 9, p1697
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let $\mathcal{M}$ and $\mathcal{N}$ be the von Neumann algebras induced by the rational action of the group SL(ℝ) and its subgroup P on the upper half plane $\mathbb{H}$. We have shown that $\mathcal{N}$ is spatial isomorphic to the group von Neumann algebra $\mathcal{L}_P$ and characterized $\mathcal{M}$ and its commutant $\mathcal{M}'$ and gotten a generalization of the Mautner's lemma. It is also shown that the Berezin operator commutates with the Laplacian operator.
ACCESSION #
64458767

 

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