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

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Muon capture on light nuclei

This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A=3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9) s^{-1} for A=3, where the uncertainties arise from the adopted fitting procedure.Comment: 6 pages, submitted to Few-Body Sys

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

The significance of seniority for women managers’ interpretations of organizational restructuring

This paper examines the impact of restructuring within the transport and logistics sector on women managers working at senior and less senior (middle/junior management) levels of the organization. The majority of women experienced increased performance pressures and heavier workloads as well as an increase in working hours. At the same time, there were pressures to work at home (i.e. week-ends and evenings) and reduced opportunities to work from home (i.e. during normal office hours). Management level emerged as an important factor in how these changes were interpreted. Senior managers perceived more positive outcomes in terms of increased motivation and loyalty. Despite a longer working week, they were less likely to report low morale as an outcome from long hours. In fact, irrespective of management level, women working shorter hours were more likely to report low morale as an outcome. Results are discussed in relation to literature on restructuring and careers, in terms of perceptual framing and in relation to different levels of investment in the organization

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

What’s sex got to do with it? A family-based investigation of growing up heterosexual during the twentieth century

This paper explores findings from a cross-generational study of the making of heterosexual relationships in East Yorkshire, which has interviewed women and men within extended families. Using a feminist perspective, it examines the relationship between heterosexuality and adulthood, focussing on sexual attraction, courtship, first kisses, first love and first sex, as mediated within family relationships, and at different historical moments. In this way, the contemporary experiences of young people growing up are compared and contrasted with those of mid-lifers and older adults who formed heterosexual relationships within the context of the changing social and sexual mores of the 1960s/1970s, and the upheavals of World War Two

Discrimination, labour markets and the Labour Market Prospects of Older Workers: What Can a Legal Case Teach us?

As governments become increasingly concerned about the fiscal implications of the ageing population, labour market policies have sought to encourage mature workers to remain in the labour force. The ‘human capital’ discourses motivating these policies rest on the assumption that older workers armed with motivation and vocational skills will be able to return to fulfilling work. This paper uses the post-redundancy recruitment experiences of former Ansett Airlines flight attendants to develop a critique of these expectations. It suggests that policies to increase older workers’ labour market participation will not succeed while persistent socially constructed age- and gender- typing shape labour demand. The conclusion argues for policies sensitive to the institutional structures that shape employer preferences, the competitive rationality of discriminatory practices, and the irresolvable tension between workers’ human rights and employers’ property rights

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category \mc{O} of the general linear superalgebra. We also prove the super duality conjecture