Classification of finite-dimensional Lie superalgebras whose even part is a three-dimensional simple Lie algebra over a field of characteristic not two or three

Let $k$ be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras $\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ over $k$, where $\mathfrak{g}_0$ is a three-dimensional simple Lie algebra. If $\mathcal{Z}(\mathfrak{g})$ denotes the centre of $\mathfrak{g}$, the result is the following: either $\lbrace \mathfrak{g}_1,\mathfrak{g}_1 \rbrace=\lbrace 0 \rbrace$ or $\mathfrak{g}_1=(\mathfrak{g}_0 \oplus k)\oplus \mathcal{Z}(\mathfrak{g})$ or $\mathfrak{g}\cong \mathfrak{osp}_k(1|2)\oplus \mathcal{Z}(\mathfrak{g})$

Raising rivals’ costs strategy: test on two LAFS in Europe

Some Localised Agro-Food Systems (LAFS) are traditionally qualified as success stories (Comté PDO in France, Gruyere PDO in Switzerland, Parmigiano Reggiano PDO in Italy), whilst other PDOs (as for example the Cantal PDO from France) pay the same price for the milk as standard milk. The price difference may reach between 10 and 25% over a long period. To explain this difference, we assume that the agents who make up the LAFS developed a collective action to protect their localized cheese production system against unfair competition and to promote their product outside its region of origin. The aim of this communication is to shed light on levers which the agents activate to assure their uniqueness is irrevocable, and uphold the benefits of their LAFS. We propose to discuss the idea that the search for market power based on the strategy of raising rivals’ costs may be used even outside a situation of vertical integration or a situation in which pressure is applied to suppliers to challenge competitors. We assume that some companies within the LAFS have sufficient control on the rules governing the organization of the traditional system to benefit from it. They also succeed in protecting a kind of relationship between business companies. The Raising Rivals’ Costs theory helps to analyze the economic consequences of the legal set-up implementation and of its control by some companies. Indeed, we show that the collective control of the rules which are set up in the PDO legal framework explain the difficulties met by rivals to stand out through an alternative and independent production system based on the costs leadership strategy. The collective set up of institutions and rules help the agents to achieve a collective competitive advantage in which every agent benefits individually. This is the strategy developed in Europe and particularly for two PDO Localised Agro-cheese Systems: Comté PDO for France and Gruyère PDO for Switzerland.PDO, localised agro-food system, Raising rivals’ costs, regulation, Agribusiness, Agricultural and Food Policy, Community/Rural/Urban Development, Food Consumption/Nutrition/Food Safety, Labor and Human Capital,

RAISING RIVALS’ COSTS STRATEGYAND LOCALISED AGRO-FOOD SYSTEMS IN EUROPE

For some Localised Agro-Food Systems (LAFS), for ex. Comté in France, Gruyère in Switzerland, the cheese and milk prices are above average whilst others as for example the Cantal from France are similar or even below average. The objective of this paper is to shed light on levers which the agents activate to assure their uniqueness is irrevocable, and uphold the benefits of their LAFS. Raising Rivals' Costs Theory gives interesting point of view about the behaviour of firms which could make use of the collective rules to raise the costs of their competitors in the particular case of LAFS oriented to the production of traditional cheeses. This will be explored through two cases studies. In the first case (territorial collective governance mode of the local supply chain), the conditions are met to conclude that the raising costs strategy corresponds to requirements which are based to a corresponding quality which meets consumers’ expectations and willingness to pay. In the second case (sectoral governance mode), few firms have taken control on the supply chain and have imposed with the time a model based on costs leadership. As conclusion, a case-by-case in-depth approach is necessary to assess whether strategy to raise costs of the rivals damages consumers welfare in the case of PDO supply chains.PDO, localised agro-food system, Raising Rivals’ Costs, governance of LAFS, Agribusiness,

Mixed Bundling Auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling

Involutions of sl(2,k) and non-split, three-dimensional simple Lie algebras

We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-split three-dimensional simple Lie algebras obtained in this way are parametrised by a subgroup of the Brauer group of k and are characterised by the fact that their Killing form represents -2. Over local and global fields we re-express this condition in terms of Hilbert and Legendre Symbols and give examples of three-dimensional simple Lie algebras which can and cannot be obtained by this construction over the field of rationals

The Kostant invariant and special ε-orthogonal representations for ε-quadratic colour Lie algebras

Let k be a field of characteristic not two or three, let $\mathfrak{g}$ be a finite-dimensional colour Lie algebra and let V be a finite-dimensional representation of $\mathfrak{g}$. In this article we give various ways of constructing a colour Lie algebra $\tilde{\mathfrak{g}}$ whose bracket in some sense extends both the bracket of $\mathfrak{g}$ and the action of $\mathfrak{g}$ on V. Colour Lie algebras, originally introduced by R. Ree ([Ree60]), generalise both Lie algebras and Lie superalgebras, and in those cases our results imply many known results ([Kos99], [Kos01], [CK15], [SS15]). For a class of representations arising in this context we show there are covariants satisfying identities analogous to Mathews identities for binary cubics

Geometric properties of special orthogonal representations associated to exceptional Lie superalgebras

From an octonion algebra $\mathbb{O}$ over a field $k$ of characteristic not two or three, we show that the fundamental representation ${\rm Im}(\mathbb{O})$ of the derivation algebra ${\rm Der}(\mathbb{O})$ and the spinor representation $\mathbb{O}$ of $\mathfrak{so}({\rm Im}(\mathbb{O}))$ are special orthogonal representations. They have particular geometric properties coming from their similarities with binary cubics and we show that the covariants of these representations and their Mathews identities are related to the Fano plane and the affine space $(\mathbb{Z}_2)^3$. This also permits to give constructions of exceptional Lie superalgebras.Comment: 16 page

Kinetic self-organization of trenched templates for the fabrication of versatile ferromagnetic nanowires

We have self-organized versatile magnetic nanowires, ie with variable period and adjustable magnetic anisotropy energy (MAE). First, using the kinetic roughening of W(110) uniaxial templates of trenches were grown on commercial Sapphire wafers. Unlike most templates used for self-organization, those have a variable period, 4-12nm are demonstrated here. Fe deposition then results in the formation of wires in the trenches. The magnitude of MAE could be engineered up or down by changing the capping- or underlayer, in turn affecting the mean superparamagnetic temperature, raised to 175K so far.Comment: 3 page

Morphological operators for very low bit rate video coding

This paper deals with the use of some morphological tools for video coding at very low bit rates. Rather than describing a complete coding algorithm, the purpose of this paper is to focus on morphological connected operators and segmentation tools that have proved to be attractive for compression.Peer ReviewedPostprint (published version

Mixed Bundling Auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.