Relative commutants of strongly self-absorbing C∗-algebras

Peer reviewed

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

Realising the cup product of local Tate duality

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p^2 whose class in the Brauer group gives the cup product f\cup g. This algebra is as small as possible.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Experimenting with infinite groups, I

A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

Mesozoic sequence of Fuerteventura (Canary Islands): Witness of Early Jurassic sea-floor spreading in the central Atlantic

The Fuerteventura Jurassic sedimentary succession consists of oceanic and elastic deposits, the latter derived from the southwestern Moroccan continental margin. Normal mid-oceanic-ridge basalt (N-MORB) flows and breccias are found at the base of the sequence and witness sea-floor spreading events in the central Atlantic. These basalts were extruded in a postrift environment (post-late Pliensbachian), We propose a Toarcian age for the Atlantic oceanic floor in this region, on the basis of the presence higher up in the sequence of the Bositra buchi filament microfacies (Aalenian-Bajocian) and of elastic deposits reflecting tectono-eustatic events (e.g,, late Toarcian to mid-Callovian erosion of the rift shoulder). The S-l sea-floor oceanic magnetic anomaly west of Fuerteventura is therefore at least Toarcian in age. The remaining sequence records Atlantic-Tethyan basinal facies (e.g., Callovian-Oxfordian red clays, Aptian-Albian black shales) alternating with elastic deposits (e.g., Kimmeridgian-Berriasian periplatform calciturbidites and a Lower Cretaceous deep-sea fan system). The Fuerteventura N-MORB outcrops represent the only Early Jurassic oceanic basement described so far in the central Atlantic. They are covered by a 1600 m, nearly continuous sedimentary sequence which extends to Upper Cretaceous facies.

Genotyping hepatitis C virus from hemodialysis patients in Central Brazil by line probe assay and sequence analysis

The present study examined the distribution of hepatitis C virus (HCV) genotypes and subtypes in a hemodialysis population in Goiás State, Central Brazil, and evaluated the efficiency of two genotyping methods: line probe assay (LiPA) based on the 5' noncoding region and nucleotide sequencing of the nonstructural 5B (NS5B) region of the genome. A total of 1095 sera were tested for HCV RNA by RT-nested PCR of the 5' noncoding region. The LiPA assay was able to genotype all 131 HCV RNA-positive samples. Genotypes 1 (92.4%) and 3 (7.6%) were found. Subtype 1a (65.7%) was the most prevalent, followed by subtypes 1b (26.7%) and 3a (7.6%). Direct nucleotide sequencing of 340 bp from the NS5B region was performed in 106 samples. The phylogenetic tree showed that 98 sequences (92.4%) were classified as genotype 1, subtypes 1a (72.6%) and 1b (19.8%), and 8 sequences (7.6%) as subtype 3a. The two genotyping methods gave concordant results within HCV genotypes and subtypes in 100 and 96.2% of cases, respectively. Only four samples presented discrepant results, with LiPA not distinguishing subtypes 1a and 1b. Therefore, HCV genotype 1 (subtype 1a) is predominant in hemodialysis patients in Central Brazil. By using sequence analysis of the NS5B region as a reference standard method for HCV genotyping, we found that LiPA was efficient at the genotype level, although some discrepant results were observed at the subtype level (sensitivity of 96.1% for subtype 1a and 95.2% for subtype 1b). Thus, analysis of the NS5B region permitted better discrimination between HCV subtypes, as required in epidemiological investigations.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Ramond-ramond central charges in the supersymmetry algebra of the superstring

The free action for the massless sector of the type II superstring was recently constructed using closed Ramond-Neveo-Schwarz superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N = 2 D = 10 supersymmetry algebra with Ramond-Ramond central charges.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.