Modular Categories Associated to Unipotent Groups

Let G be a unipotent algebraic group over an algebraically closed field k of characteristic p > 0 and let l be a prime different from p. Let e be a minimal idempotent in D_G(G), the braided monoidal category of G-equivariant (under conjugation action) \bar{Q_l}-complexes on G. We can associate to G and e a modular category M_{G,e}. In this article, we prove that the modular categories that arise in this way from unipotent groups are precisely those in the class C_p^{\pm}.Comment: 26 page

Organic farming systems benefit biodiversity and natural pest regulation in white cabbage

Natural regulation of cabbage root flies works well in experimental organic cropping systems of white cabbage. Low input and complex organic systems benefit functional biodiversity by providing good living conditions to several groups of natural enemies. Intercropped green manure benefits large predators while small predatory beetles favour low input organic systems with bare soil between crop rows

Simplification Techniques for Maps in Simplicial Topology

This paper offers an algorithmic solution to the problem of obtaining "economical" formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used for defining cohomology operations at the cochain level. As an example, we obtain explicit combinatorial descriptions of Steenrod k-th powers exclusively in terms of face operators

Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Non-commutative connections of the second kind

A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a differentiable bimodule is described. The curvature for a hom-connection is defined, and it is shown that flat hom-connections give rise to a chain complex.Comment: 13 pages, LaTe

Remarks on 2-dimensional HQFT's

We introduce and study algebraic structures underlying 2-dimensional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner, and the second author on 2-dimensional HQFTs with simply-connected or aspherical targets.Comment: 22 pages, 14 figures. In this version we added a detailed proof for Theorem 3.3 and made some minor corrections

Computing the homology of groups: the geometric way

In this paper we present several algorithms related with the computation of the homology of groups, from a geometric perspective (that is to say, carrying out the calculations by means of simplicial sets and using techniques of Algebraic Topology). More concretely, we have developed some algorithms which, making use of the effective homology method, construct the homology groups of Eilenberg-MacLane spaces K(G,1) for different groups G, allowing one in particular to determine the homology groups of G. Our algorithms have been programmed as new modules for the Kenzo system, enhancing it with the following new functionalities: - construction of the effective homology of K(G,1) from a given finite free resolution of the group G; - construction of the effective homology of K(A,1) for every finitely generated Abelian group A (as a consequence, the effective homology of K(A,n) is also available in Kenzo, for all n); - computation of homology groups of some 2-types; - construction of the effective homology for central extensions. In addition, an inverse problem is also approached in this work: given a group G such that K(G,1) has effective homology, can a finite free resolution of the group G be obtained? We provide some algorithms to solve this problem, based on a notion of norm of a group, allowing us to control the convergence of the process when building such a resolution

Insect pathogenic fungi in biological control: status and future challenges

In Europe, insect pathogenic fungi have in decades played a significant role in biological control of insects. With respect to the different strategies of biological control and with respects to the different genera of insect pathogenic fungi, the success and potential vary, however. Classical biological control: no strong indication of potential. Inundation and inoculation biological control: success stories with the genera Metarhizium, Beauveria, Isaria/Paecilomyces and Lecanicillium (previously Verticillium). However, the genotypes employed seem to include a narrow spectrum of the many potentially useful genotypes. Conservation biological control: Pandora and Entomophthora have a strong potential, but also Beauveria has a potential to be explored further. The main bottleneck for further exploitation of insect pathogenic fungi in biological control is the limited knowledge of host pathogen interaction at the fungal genotype level

A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Delimiting Deviance: Visual and Verbal Representations of Scandal on British TV News

When moral boundaries are defined, TV news storytelling plays an important role. This paper explores the visual and verbal markers that construct the categories of right and wrong, normal and deviant, us and them. By stressing the bonds between ‘the media’ and ‘the public’, TV storytellers assume the legitimacy to frame and represent social reality. Traditionally, the media have pointed out deviance among the lower strata of the population, but powerful individuals and institutions are increasingly identified as wrongdoers. Using the Mid Staffs hospital scandal as a case study, this article examines how TV news employ scandal to describe deviance in the higher echelons of society and the exposure of the wrongdoings to ‘us’, the public. This process takes place on several levels, from visual and verbal storytelling to shifting cultural and social structures. How these moral tales and social shifts influence each other is a central part of the discussion here. The boundary between normal and deviant behaviour is changing, influencing both the way people think about themselves and the societies they live in