Central sequences in the factor associated with Thompson’s group $F$

Paul Jolissaint

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Displaying similar documents to “Central sequences in the factor associated with Thompson’s group $F$ ”

Automorphisms of central extensions of type I von Neumann algebras

Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2011)

Studia Mathematica

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Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as $T = T_{a} \circ T_{ϕ}$ , where $T_{a} (x) = a x a^{- 1}$ is an inner automorphism implemented by an element a ∈ E(M), and $T_{ϕ}$ is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type $I_{\infty}$ then every band preserving...

Equivalence bimodule between non-commutative tori

Sei-Qwon Oh, Chun-Gil Park (2003)

Czechoslovak Mathematical Journal

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The non-commutative torus $C^{*} (ℤ^{n}, ω)$ is realized as the $C^{*}$ -algebra of sections of a locally trivial $C^{*}$ -algebra bundle over $\hat{S_{ω}}$ with fibres isomorphic to $C^{*} (ℤ^{n} / S_{ω}, ω_{1})$ for a totally skew multiplier $ω_{1}$ on $ℤ^{n} / S_{ω}$ . D. Poguntke [9] proved that $A_{ω}$ is stably isomorphic to $C (\hat{S_{ω}}) \otimes C^{*} (ℤ^{n} / S_{ω}, ω_{1}) ≅ C (\hat{S_{ω}}) \otimes A_{ϕ} \otimes M_{k l} (ℂ)$ for a simple non-commutative torus $A_{ϕ}$ and an integer $k l$ . It is well-known that a stable isomorphism of two separable $C^{*}$ -algebras is equivalent to the existence of equivalence bimodule between them. We construct an $A_{ω}$ - $C (\hat{S_{ω}}) \otimes A_{ϕ}$ -equivalence bimodule.

A $C^{*}$ -algebraic Schoenberg theorem

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Donald W. Robinson (1984)

Annales de l'institut Fourier

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Let $𝔄$ be a $C^{*}$ -algebra, $G$ a compact abelian group, $τ$ an action of $G$ by $*$ -automorphisms of $𝔄, 𝔄^{τ}$ the fixed point algebra of $τ$ and $𝔄_{F}$ the dense sub-algebra of $G$ -finite elements in $𝔄$ . Further let $H$ be a linear operator from $𝔄_{F}$ into $𝔄$ which commutes with $τ$ and vanishes on $𝔄^{τ}$ . We prove that $H$ is a complete dissipation if and only if $H$ is closable and its closure generates a $C_{0}$ -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative...

$C^{*}$ algebras associated with von Neumann algebras

Tullio G. Ceccherini-Silberstein (1999)

Bollettino dell'Unione Matematica Italiana

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Ad un'algebra di von Neumann separabile $M$ , in forma standard su di uno spazio di Hilbert $H$ , si associa la $C^{*}$ algebra $O_{M}$ definita come la $C^{*}$ algebra $O_{U (M)}$ costituita dai punti fissi dell'algebra di Cuntz generalizzata $O_{H}$ mediante l'azione canonica del gruppo $U (M)$ degli unitari di $M$ . Si dà una caratterizzazione di $O_{M}$ nel caso in cui $M$ è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se $ω$ è uno stato vettoriale normale e fedele...

L²-homology and reciprocity for right-angled Coxeter groups

Boris Okun, Richard Scott (2011)

Fundamenta Mathematicae

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Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra $_{μ}$ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define $L ²_{μ}$ -Betti numbers and an $L ²_{μ}$ -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version...

Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb, Filip Strobin (2015)

Colloquium Mathematicae

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We consider the following notion of largeness for subgroups of $S_{\infty}$ . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of $S_{\infty}$ can be extended to a large free subgroup of $S_{\infty}$ , and, under Martin’s Axiom, any free subgroup of $S_{\infty}$ of cardinality less than can also be extended to a large free subgroup of $S_{\infty}$ . Finally, if Gₙ are countable...

Factoriality of von Neumann algebras connected with general commutation relations-finite dimensional case

Ilona Królak (2006)

Banach Center Publications

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We study a certain class of von Neumann algebras generated by selfadjoint elements $ω_{i} = a_{i} + a ⁺_{i}$ , where $a_{i}, a ⁺_{i}$ satisfy the general commutation relations: $a_{i} a ⁺_{j} = \sum_{r, s} t_{j}^{i} r_{s} a ⁺_{r} a_{s} + δ_{i j} I d$ . We assume that the operator T for which the constants $t_{j}^{i} r_{s}$ are matrix coefficients satisfies the braid relation. Such algebras were investigated in [BSp] and [K] where the positivity of the Fock representation and factoriality in the case of infinite dimensional underlying space were shown. In this paper we prove that under certain conditions on the...

The Hughes subgroup

Robert Bryce (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common...

The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd $n \geq 665$ and even $n = 16 k \geq 8000$ .

Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti, Paulo R. Pinto (2011)

Banach Center Publications

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We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that $A \otimes_{m i n} B$ inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove...

Sets of p-multiplicity in locally compact groups

I. G. Todorov, L. Turowska (2015)

Studia Mathematica

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We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if $E * = (s, t) : t s^{- 1} \in E$ is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.

Displaying similar documents to “Central sequences in the factor associated with Thompson’s group F ”

Displaying similar documents to “Central sequences in the factor associated with Thompson’s group $F$ ”