4,295 research outputs found
A Mixing Property for the Action of SL(3,Z) × SL(3,Z) on the Stone–Čech Boundary of SL(3,Z)
No full textBy analogy with the construction of the Furstenberg boundary, the Stone- C?ech boundary of SL(3, 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 that belong to specific regions, defined in terms of flags. We show that the SL(3, Z) x SL(3, Z)-quasi-invariant Radon measures supported on these regions are tempered. Thus, every quasi-invariant Radon boundary measure for SL(3, Z) is an orthogonal sum of a tempered measure and a measure having matrix coefficients belonging to a certain ideal c' (0)((SL(3, Z) x SL(3, Z)), slightly larger than c(0)((SL(3, Z) x SL(3, Z)). Hence, the left-right representation of C-*(SL(3, Z) x SL(3, Z)) in the Calkin algebra of SL(3, Z) factors through C-* (c' 0)(SL(3, Z) x SL(3, Z)) and the centralizer of every infinite subgroup of SL(3, Z) is amenable
A mixing property for the action of \SL(3,\mathbb{Z})\times\SL(3,\mathbb{Z}) on the Stone-Cech boundary of \SL(3,\mathbb{Z})
No full textBy 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.Comment: There was a flow in an argument in Section 4 of the previous version
and the main results have been slightly modified accordingly. Accepted
version, to appear in Int. Math. Res. Not. IMR
On -Algebras associated to Horocycle Flows
No full textThis thesis is mainly concerned with the study of the crossed product -algebras associated to the horocycle flow on compact quotients of \SL(2,\rr). Looking at the Cuntz semigroup, we retrieve some information about the structure of hereditary -subalgebras and Hilbert modules for a class of -algebras which contain the -algebras we want to study. After translating these results in our context, we study the functoriality of the construction both for the case of discrete subgroups of \SL(2,\rr) and for the case of hyperbolic Riemann surfaces. Also properties of another crossed product -algebra that is Morita equivalent to the -algebra of the horocycle flow are explored and from considerations about the associated dynamical system we can prove that the multiplier algebra of the crossed product -algebra associated to the horocyce flow contains a Kirchberg algebra in the UCT class as a unital -subalgebra in some cases.\\
A side chapter is devoted to a project that the author started during his PhD, concerning the construction of spectral triples on the Jiang-Su algebra. The construction we give is performed by means of a particular -embedding
An example of a non-amenable dynamical system which is boundary amenable
No full textIt is shown that the action of SL(3, Z) on the Stone-Cech boundary of SL(3, Z)/SL(2, Z) is amenable. This confirms a prediction by Bekka and Kalantar [Trans. Amer. Math. Soc. 373 (2020), pp. 2105-2133]
On -algebras associated to actions of discrete subgroups of on the punctured plane
No full textDynamical conditions that guarantee stability for discrete transformation group -algebras are determined. The results are applied to the case of some discrete subgroups of acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the -algebra associated to the horocycle flow on the corresponding compact homogeneous space of
CR1 Knops blood group alleles are not associated with severe malaria in the Gambia
No full textThe Knops blood group antigen erythrocyte polymorphisms have been associated with reduced falciparum malaria-based in vitro rosette formation (putative malaria virulence factor). Having previously identified single-nucleotide polymorphisms (SNPs) in the human complement receptor 1 (CR1/CD35) gene underlying the Knops antithetical antigens Sl1/Sl2 and McC(a)/McC(b), we have now performed genotype comparisons to test associations between these two molecular variants and severe malaria in West African children living in the Gambia. While SNPs associated with Sl:2 and McC(b+) were equally distributed among malaria-infected children with severe malaria and control children not infected with malaria parasites, high allele frequencies for Sl 2 (0.800, 1,365/1,706) and McC(b) (0.385, 658/1706) were observed. Further, when compared to the Sl 1/McC(a) allele observed in all populations, the African Sl 2/McC(b) allele appears to have evolved as a result of positive selection (modified Nei-Gojobori test Ka-Ks/s.e.=1.77, P-valu
Quantum and its irreducible representations
No full textWe define for real a unital -algebra
quantizing the universal enveloping
-algebra of . The -algebra
is realized as a -subalgebra of the
Drinfeld double of and its dual Hopf -algebra
, generated by the equatorial Podle\'s sphere coideal
-subalgebra of and
its associated orthogonal coideal -subalgebra . We then classify all the irreducible
-representations of .Comment: 22 pages; author accepted manuscrip
On the sheaf-theoretic SL(2, C) Casson–Lin invariant
No full textWe prove that the (τ-weighted, sheaf-theoretic) SL(2, C) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology and algebraic geometry, and rely crucially on the fact that the SL(2, C) Casson–Lin invariant admits an alternative interpretation via the theory of Behrend functions.</p
Pulsed laser deposition of single-layer MoS2 on Au(111): from nanosized crystals to large-area films
No full textMolybdenum disulphide (MoS2) is a promising material for heterogeneous catalysis and novel twodimensional (2D) optoelectronic devices. In this work, we synthesized single-layer (SL) MoS2 structures on Au(111) by pulsed laser deposition (PLD) under ultra-high vacuum (UHV) conditions. By controlling the PLD process, we were able to tune the sample morphology from low-coverage SL nanocrystals to largearea SL films uniformly wetting the whole substrate surface. We investigated the obtained MoS2 structures at the nanometer and atomic scales by means of in situ scanning tunneling microscopy/ spectroscopy (STM/STS) measurements, to study the interaction between SL MoS2 and Au(111)—which for example influences MoS2 lattice orientation—the structure of point defects and the formation of inplane MoS2/Au heterojunctions. Raman spectroscopy, performed ex situ on large-area SL MoS2, revealed significant modifications of the in-plane E1 2g and out-of-plane A1g vibrational modes, possibly related to strain and doping effects. Charge transfer between SL MoS2 and Au is also likely responsible for the total suppression of excitonic emission, observed by photoluminescence (PL) spectroscopy
Candidatus Rhetoricae (or Novus Candidatus).
No full textThis little book is a find whatever it finally turns out to be! For now it seems to be a Jesuit collegium text in rhetoric following the Progymnasmata of Aphthonius. If one works from the back of the book, there is an apparently independent 48-page work, Angelus Pacis by Nicolas Caussini (Latinized name), S.J. The rest of the book seems to be a commentary on or presentation of Aphthonius' Progymnasmata in 3 parts covering 435 pages, followed by a T of C and an AI, which is often one page off. Pars II is titled Rhetoricae Praecepta, Pars III De Panegyrico seu Laudatione. Pars I seems to be Apparatus ad Fabulam et Narrationem. Fable is handled on 15-31. After the famous Greek definition of Theion done into Latin ( sermo falsus veritatem effingens ), the author distinguishes rational (human) and moral (animal) fables, with mixed fables including both. He holds (19) that the sense of the fable generally needs to be expressed; otherwise people often miss the point of a fable. His Latin for promythium is praefabulatio, for epimythium affabulatio. Apologus and parabola are identical for him with fabula. After describing the qualities and uses of fables, the author presents some nine fables that exemplify various levels of style, twice telling the same stories on two levels (WL and FC). The last example is of the florid style: The Silkworm and the Spider takes four pages to tell! I found this book sitting in a box of disparate, unmarked, old books. It pays to look!This is a hardbound book (hard cover)Language note: Bilingual: Greek/LatinElzevers
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