Appendix to ``Regularity of Villadsen algebras'': The failure of the Corona Factorization Property for the Villadsen algebra $\mathcal{V}_\infty$

2018 ◽  
Vol 123 (1) ◽  
pp. 142-146
Author(s):  
Joan Bosa ◽  
Martin S. Christensen
Keyword(s):  
Factorization Property ◽  
Central Sequence

In this appendix to M. S. Christensen, “Regularity of Villadsen algebras and characters on their central sequence algebras”, Math. Scand. ?? (????), ???--???, we prove that the Villadsen algebra $\mathcal{V} _\infty $ does not satisfy the Corona Factorization Property (CFP).

scholarly journals When central sequence C*-algebras have characters

2015 ◽  
Vol 26 (07) ◽  
pp. 1550049 ◽  
Author(s):  
Eberhard Kirchberg ◽  
Mikael Rørdam
Keyword(s):  
Factorization Property ◽  
Tensor Power ◽  
C Algebra ◽  
Central Sequence ◽  
C Algebras ◽  
Regularity Properties ◽  
Sequence Algebra ◽  
Divisibility Properties

We investigate C*-algebras whose central sequence algebra has no characters, and we raise the question if such C*-algebras necessarily must absorb the Jiang–Su algebra (provided that they also are separable). We relate this question to a question of Dadarlat and Toms if the Jiang–Su algebra always embeds into the infinite tensor power of any unital C*-algebra without characters. We show that absence of characters of the central sequence algebra implies that the C*-algebra has the so-called strong Corona Factorization Property, and we use this result to exhibit simple nuclear separable unital C*-algebras whose central sequence algebra does admit a character. We show how stronger divisibility properties on the central sequence algebra imply stronger regularity properties of the underlying C*-algebra.

scholarly journals Regularity of Villadsen algebras and characters on their central sequence algebras

2018 ◽  
Vol 123 (1) ◽  
pp. 121-141
Author(s):  
Martin S. Christensen
Keyword(s):  
Stable Rank ◽  
Factorization Property ◽  
Central Sequence ◽  
Tracial State ◽  
Finite Dimensional ◽  
Cw Complex ◽  
Sequence Algebra ◽  
Unital Simple

We show that if $A$ is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of $A$ does not admit characters.Additionally, in a joint appendix with Joan Bosa (see the following paper), we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear $C^\ast $-algebra with a unique tracial state which fails to have this property.

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

Interference in vimentin assembly in vitro by synthetic peptides derived from the vimentin head domain

1992 ◽  
Vol 101 (3) ◽  
pp. 687-700
Author(s):  
I. Hofmann ◽  
H. Herrmann
Keyword(s):  
Synthetic Peptides ◽  
Genetically Engineered ◽  
Binding Domain ◽  
Binding Assays ◽  
Central Sequence ◽  
Amino Terminal ◽  
Molar Excess ◽  
Drastic Increase ◽  
Head Positions

The importance of the amino-terminal domain (“head”) of type III intermediate filament (IF) proteins in IF assembly has been examined by testing the influence of synthetic peptides representing a highly conserved decameric motif, KSSSYRRIMFGG, located near the amino terminus of vimentin. When added to soluble vimentin subunits this peptide induces, at fourfold molar excess or slightly above, the appearance of short, regular rod-like structures as determined by electron microscopy of negatively stained and rotary-shadowed preparations as well as by viscometry. At higher peptide concentrations large, irregularly shaped aggregates of mostly non-IF structures formed, but this aggregation was reversible by prolonged dialysis against low ionic strength buffer. The aggregating effect of this peptide was highly sequence-specific and was not seen with point-mutated sequences such as RR----TR or with unrelated peptides containing a central diarginine, indicating that it is not simply ionic. When different hexapeptides representing different “head” positions were compared, only the central sequence, SYRRXF, was as effective as the decamer. The addition of peptide during IF assembly did not prevent filament formation, although 50-fold molar excess of peptide resulted in a drastic increase (up to 40 nm) in the width of the filaments, which also appeared less regular, thus reflecting some interference with assembly. In contrast to the effects on soluble vimentin, the decameric peptide did not disturb IFs, indicating that the binding domain is “masked” or stabilized in the filaments. To identify the domain to which the peptide binds, three different binding assays using vimentin fragments and genetically engineered vimentin deletion mutants were employed. The results indicate that the binding domain of the near-amino-terminal peptide is located at the start of the alpha-helical “rod” domain of the protein. Possible mechanisms of interaction of these two portions of vimentin during IF assembly are discussed.

Central Sequence Algebras of a Purely Infinite Simple C*-algebra

2004 ◽  
Vol 56 (6) ◽  
pp. 1237-1258 ◽  
Author(s):  
Akitaka Kishimoto
Keyword(s):  
Fixed Point ◽  
Partial Isometry ◽  
Characterization Result ◽  
C Algebra ◽  
Central Sequence ◽  
Sequence Algebra ◽  
K Theory

AbstractWe are concerned with a unital separable nuclear purely infinite simple C*-algebra A satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in A are equivalent by a central partial isometry. Our second result shows that the K-theory of the central sequence algebra A′ ∩ Aω (for an ω ∈ βN\N) and its fixed point algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].

scholarly journals Unique factorization in polynomial rings with zero divisors

2020 ◽  
pp. 2150113 ◽  
Author(s):  
D. D. Anderson ◽  
Ranthony A. C. Edmonds
Keyword(s):  
Commutative Ring ◽  
Polynomial Ring ◽  
Commutative Rings ◽  
Polynomial Rings ◽  
Unique Factorization ◽  
Factorization Property ◽  
Zero Divisors ◽  
Unique Factorization Domain

Given a certain factorization property of a ring [Formula: see text], we can ask if this property extends to the polynomial ring over [Formula: see text] or vice versa. For example, it is well known that [Formula: see text] is a unique factorization domain if and only if [Formula: see text] is a unique factorization domain. If [Formula: see text] is not a domain, this is no longer true. In this paper, we survey unique factorization in commutative rings with zero divisors, and characterize when a polynomial ring over an arbitrary commutative ring has unique factorization.

scholarly journals Topological generation results for free unitary and orthogonal groups

2019 ◽  
Vol 31 (01) ◽  
pp. 2050003
Author(s):  
Alexandru Chirvasitu
Keyword(s):  
Unitary Group ◽  
Free Groups ◽  
Orthogonal Groups ◽  
Factorization Property ◽  
Residually Finite ◽  
Inductive Proof ◽  
Classical Counterpart ◽  
Lower Rank ◽  
Maximal Tori ◽  
Finiteness Properties

We show that for every [Formula: see text] the free unitary group [Formula: see text] is topologically generated by its classical counterpart [Formula: see text] and the lower-rank [Formula: see text]. This allows for a uniform inductive proof that a number of finiteness properties, known to hold for all [Formula: see text], also hold at [Formula: see text]. Specifically, all discrete quantum duals [Formula: see text] and [Formula: see text] are residually finite, and hence also have the Kirchberg factorization property and are hyperlinear. As another consequence, [Formula: see text] are topologically generated by [Formula: see text] and their maximal tori [Formula: see text] (dual to the free groups on [Formula: see text] generators) and similarly, [Formula: see text] are topologically generated by [Formula: see text] and their tori [Formula: see text].

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