CENTRAL SEQUENCES IN SUBHOMOGENEOUS UNITAL C*-ALGEBRAS

Suppose that $\mathcal {A}$ is a unital subhomogeneous C*-algebra. We show that every central sequence in $\mathcal {A}$ is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in $\mathcal {A}$ is trivial if and only if every pointwise limit of irreducible representations is irreducible. Finally, we give a nice representation of the latter algebras.

INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES

We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group.

Inner amenability for groups and central sequences in factors

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin [Groups with hyperbolically embedded subgroups. Algebr. Geom. Topol.13 (2013), 2635–2665], our result recovers that mapping class groups and $\text{Out}(\mathbb{F}_{n})$ are not inner amenable. We also show that the group-measure space constructions associated to free, strongly ergodic p.m.p. actions of such groups do not have property Gamma of Murray and von Neumann [On rings of operators IV. Ann. of Math. (2) 44 (1943), 716–808].

Highly Ordered Spatial Organization of the Structural Long Noncoding NEAT1 RNAs within Paraspeckle Nuclear Bodies

Paraspeckles (PSPs) are nuclear bodies associated with the retention in the nucleus of specific mRNAs. Two isoforms of a long noncoding RNA (NEAT1_v1/Menε and NEAT1_v2/Menβ) are required for the integrity of PSPs. Here, we analyzed the molecular organization of PSPs by immuno- and in situ hybridization electron microscopy. Detection of the paraspeckle markers PSPC1 and P54NRB/NONO confirm the identity between PSPs and the previously described interchromatin granule-associated zones (IGAZs). High-resolution in situ hybridization of NEAT1 transcripts revealed a highly ordered organization of IGAZ/PSPs. Although the 3.7-kb NEAT1_v1 and the identical 5′ end of the 22.7-kb NEAT1_v2 transcripts are confined to the periphery, central sequences of NEAT1_v2 are found within the electron-dense core of the bodies. Moreover, the 3′ end of NEAT1_v2 also localize to the periphery, indicating possible architectures for IGAZ/PSPs. These results further suggest that the organization of NEAT1 transcripts constrains the geometry of these bodies. Accordingly, we observed in HeLa and NIH 3T3 cells that IGAZ/PSPs are elongated structures with a well-defined diameter. Our results provide new insight on the ability of noncoding RNAs to form subcellular structures.

COMMUTING SQUARE SUBFACTORS AND CENTRAL SEQUENCES

Let M0 ⊂ M1 be a finite index infinite depth hyperfinite II 1 subfactor and ω a free ultrafilter of the natural numbers. We show that if this subfactor is constructed from a commuting square then the central sequence inclusion [Formula: see text] has infinite Pimsner–Popa index. We will also demonstrate this result for certain infinite depth hyperfinite subfactors coming from groups.

Operator algebras related to Thompson's group F

Let F′ be the commutator subgroup of F and let Γ0 be the cyclic group generated by the first generator of F. We continue the study of the central sequences of the factor L(F′), and we prove that the abelian von Neumann algebra L(Γ0) is a strongly singular MASA in L(F). We also prove that the natural action of F on [0, 1] is ergodic and that its ratio set is {0} ∪ {2k; k ∞ Z}.

Complete sequence of the human mucin MUC4: a putative cell membrane-associated mucin

The MUC4 gene, which encodes a human epithelial mucin, is expressed in various epithelial tissues, just as well in adult as in poorly differentiated cells in the embryo and fetus. Its N-terminus and central sequences have previously been reported as comprising a 27-residue peptide signal, followed by a large domain varying in length from 3285 to 7285 amino acid residues. The present study establishes the whole coding sequence of MUC4 in which the C-terminus is 1156 amino acid residues long and shares a high degree of similarity with the rat sialomucin complex (SMC). SMC is a heterodimeric glycoprotein complex composed of mucin (ascites sialoglycoprotein 1, ASGP-1) and transmembrane (ASGP-2) subunits. The same organization is found in MUC4, where the presence of a GlyAspProHis proteolytic site may cleave the large precursor into two subunits, MUC4α and MUC4β. Like ASGP-2, which binds the receptor tyrosine kinase p185neu, MUC4β possesses two epidermal growth factor-like domains, a transmembrane sequence and a potential phosphorylated site. MUC4, the human homologue of rat SMC, may be a heterodimeric bifunctional cell-surface glycoprotein of 2.12 µm. These results confer a new biological role for MUC4 as a ligand for ErbB2 in cell signalling.