Infinitesimal deformation quantization of complex analytic spaces

Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson bracket is given. It is shown that the analytic Hochschild (co)homology on a complex space has structure of coherent analytic sheaf in each degree

On the nature of the Virasoro algebra

The multiplication in the Virasoro algebra $$[e_p, e_q] = (p - q) e_{p+q} + \theta \left(p^3 - p\right) \delta_{p + q}, \qquad p, q \in {\mathbf Z},$$ $$[\theta, e_p] = 0,$$ comes from the commutator $[e_p, e_q] = e_p * e_q - e_q * e_p$ in a quasiassociative algebra with the multiplication \renewcommand{\theequation}{$*$} \be \ba{l} \ds e_p * e_q = - {q (1 + \epsilon q) \over 1 + \epsilon (p + q)} e_{p+q} + {1 \over 2} \theta \left[p^3 - p + \left(\epsilon - \epsilon^{-1} \right) p^2 \right] \delta^0_{p+q}, \vspace{3mm}\\ \ds e_p * \theta = \theta* e_p = 0. \ea \ee The multiplication in a quasiassociative algebra ${\cal R}$ satisfies the property \renewcommand{\theequation}{$**$} \be a * (b * c) - (a * b) * c = b * (a * c) - (b * a) * c, \qquad a, b, c \in {\cal R}. \ee This property is necessary and sufficient for the Lie algebra {\it Lie}$({\cal R})$ to have a phase space. The above formulae are put into a cohomological framework, with the relevant complex being different from the Hochschild one even when the relevant quasiassociative algebra ${\cal R}$ becomes associative. Formula $(*)$ above also has a differential-variational counterpart

Researching ‘bogus’ asylum seekers, ‘illegal’ migrants and ‘crimmigrants’

Both immigration and criminal laws are, at their core, systems of inclusion and exclusion. They are designed to determine whether and how to include individuals as members of society or exclude them from it, thereby, creating insiders and outsiders (Stumpf 2006). Both are designed to create distinct categories of people — innocent versus guilty, admitted versus excluded or, as majority would say, ‘legal’ versus ‘illegal’ (Stumpf 2006). Viewed in that light, perhaps it is not surprising that these two areas of law have become inextrica- bly connected in the official discourses. When politicians and policy makers (and also law enforcement authorities and tabloid press) seek to raise the barriers for non-citizens to attain membership in society, it is unremarkable that they turn their attention to an area of the law that similarly func- tions to exclude the ‘other’ — transforming immigrants into ‘crimmigrants’.1 As a criminological researcher one then has to rise up to the challenges of disentangling these so-called officially constructed (pseudo) realities, and breaking free from a continued dominance of authoritative discourses, and developing an alternative understanding of ‘crimmigration’ by connecting the processes of criminal is ation and ‘other ing’ with poverty, xe no-racism and other forms of social exclusion (see Institute of Race Relations 1987; Richmond 1994; Fekete 2001; Bowling and Phillips 2002; Sivanandan 2002; Weber and Bowling 2004)

Continuity properties of measurable group cohomology

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic properties of group cohomology, but various analytic features of those cohomology groups were only partially understood. This paper re-examines some of those issues. At its heart is a simple dimension-shifting argument which enables one to `regularize' measurable cocycles, leading to some simplifications in the description of the cohomology groups. A range of consequences are then derived from this argument. First, we prove that for target modules that are Fr\'echet spaces, the cohomology groups agree with those defined using continuous cocycles, and hence they vanish in positive degrees when the acting group is compact. Using this, we then show that for Fr\'echet, discrete or toral modules the cohomology groups are continuous under forming inverse limits of compact base groups, and also under forming direct limits of discrete target modules. Lastly, these results together enable us to establish various circumstances under which the measurable-cochains cohomology groups coincide with others defined using sheaves on a semi-simplicial space associated to the underlying group, or sheaves on a classifying space for that group. We also prove in some cases that the natural quotient topologies on the measurable-cochains cohomology groups are Hausdorff.Comment: 52 pages. [Nov 22, 2011:] Major re-write with Calvin C. Moore as new co-author. Results from previous version strengthened and several new results added. [Nov 25, 2012:] Final version now available at springerlink.co

Observation of unusual chlorine activation by ground-based infrared and microwave spectroscopy in the late Arctic winter 2000/01

International audienceDuring the Arctic winter of 2000/01, ground-based FTIR and millimetre-wave measurements revealed significant amounts of ClO over Kiruna after the final warming in February 2001. In fact, column amounts of ClO were still increased in March 2001 when temperatures were about 20K above the PSC (Polar Stratospheric Clouds) threshold. At these temperatures, chlorine activation due to heterogeneous processes on PSCs is not possible even in the presence of strong lee wave effects. In order to discuss possible reasons of this feature, time series of other chemical species will be presented and discussed, too. Measurements of HF and COF2 indicated that vortex air was still observed in mid-March 2001. Since the time series of HNO3 column amounts do not give any evidence of a denitrification later than 11 February, chlorine activation persisting for several weeks after the presence of PSCs due to denitrification is rather unlikely. The photolysis of ClONO2-rich air which had been formed at the end of February and beginning of March 2001 as well as chlorine activation due to the presence of an unusual aerosol layer are discussed as possible causes of the increased ClO column amounts after the final warming

Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual