Non-associative Frobenius algebras for simply laced Chevalley groups

We provide an explicit construction for a class of commutative, non-associative algebras for each of the simple Chevalley groups of simply laced type. Moreover, we equip these algebras with an associating bilinear form, which turns them into Frobenius algebras. This class includes a 3876-dimensional algebra on which the Chevalley group of type E8 acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras

Decomposition algebras and axial algebras

We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field, thereby allowing repetition of eigenvalues; (2) They allow for decompositions that do not arise from multiplication by idempotents; (3) They admit a natural notion of homomorphisms, making them into a nice category. We exploit these facts to strengthen the connection between axial algebras and groups. In particular, we provide a definition of a universal Miyamoto group which makes this connection functorial under some mild assumptions. We illustrate our theory by explaining how representation theory and association schemes can help to build a decomposition algebra for a given (permutation) group. This construction leads to a large number of examples. We also take the opportunity to fix some terminology in this rapidly expanding subject.Comment: 23 page

Modules over axial algebras

We introduce axial representations and modules over axial algebras as new tools to study axial algebras. All known interesting examples of axial algebras fall into this setting, in particular the Griess algebra whose automorphism group is the Monster group. Our results become especially interesting for Matsuo algebras. We vitalize the connection between Matsuo algebras and 3-transposition groups by relating modules over Matsuo algebras with representations of 3-transposition groups. As a by-product, we define, given a Fischer space, a group that can fulfill the role of a universal 3-transposition group

Evidence of climate effects on the height-diameter relationships of tree species

International audienceAbstractKey messageThe mean temperature from March to September affects the height-diameter relationship of many tree species in France. For most of these species, the temperature effect is nonlinear, which makes the identification of an optimal temperature possible. Increases in mean temperature could impact the volume supply of commercial species by the end of the twenty-first century.ContextHeight-diameter (HD) relationships are central in forestry since they are essential to estimate tree volume and biomass. Since the late 1960s, efforts have been made to generalize models of HD relationships through the inclusion of plot- and tree-level explanatory variables. In some recent studies, climate variables such as mean annual temperature and precipitation have been found to have a significant effect on HD allometry. However, in these studies, the effects were all considered to be linear or almost linear, which supposes that there is no optimal temperature and no optimal precipitation.AimsIn this study, we tested the hypothesis that an optimum effect of temperature and precipitation exists on tree heights.MethodsWe fitted generalized models of HD relationships to 44 tree species distributed across France. To make sure that the climate variables would not hide some differences in terms of the local environment, the models included explanatory variables accounting for competition, tree social status and other plot-level factors such as slope inclination and the occurrence of harvesting in the last five years.ResultsIt turned out that the temperature effect was significant for 33 out of 44 species and an optimum was found in 26 cases. The precipitation effect was linear and was found to be significant for only seven species. Although the two climate variables did not contribute as much as the competition and the social status indices to the model fit, they were still important contributors. Under the representative concentration pathway (RCP) 2.6 and the assumptions of constant form factors and forest conditions in terms of competition and social statuses, it is expected that approximately two thirds of the species with climate-sensitive HD relationships will generally be shorter. This would induce a decrease in volume ranging from 1 to 5% for most of these species.ConclusionForest practitioners should be aware that the volume supply of some commercial species could decrease by the end of the twenty-first century. However, these losses could be partly compensated for by changes in the form factors and the species distributions

Archeologische Werfbegeleiding Veststraat - Balen. Eindrapport van het archeologisch onderzoek i.o.v. Molse Bouwmaatschappij.

Dit rapport werd ingediend bij het agentschap samen met een aantal afzonderlijke digitale bijlagen. Een aantal van deze bijlagen zijn niet inbegrepen in dit pdf document en zijn niet online beschikbaar. Sommige bijlagen (grondplannen, fotos, spoorbeschrijvingen, enz.) kunnen van belang zijn voor een betere lezing en interpretatie van dit rapport. Indien u deze bijlagen wenst te raadplegen kan u daarvoor contact opnemen met: [email protected]

Archeologische prospectie met ingreep in de bodem Asse-Kalkoven 2012, Z.N. - 2012/368 (prov. Vlaams-Brabant)

Dit rapport werd ingediend bij het agentschap samen met een aantal afzonderlijke digitale bijlagen. Een aantal van deze bijlagen zijn niet inbegrepen in dit pdf document en zijn niet online beschikbaar. Sommige bijlagen (grondplannen, fotos, spoorbeschrijvingen, enz.) kunnen van belang zijn voor een betere lezing en interpretatie van dit rapport. Indien u deze bijlagen wenst te raadplegen kan u daarvoor contact opnemen met: [email protected]

Archeologisch Proefsleuvenonderzoek Veststraat - Balen

Dit rapport werd ingediend bij het agentschap samen met een aantal afzonderlijke digitale bijlagen. Een aantal van deze bijlagen zijn niet inbegrepen in dit pdf document en zijn niet online beschikbaar. Sommige bijlagen (grondplannen, fotos, spoorbeschrijvingen, enz.) kunnen van belang zijn voor een betere lezing en interpretatie van dit rapport. Indien u deze bijlagen wenst te raadplegen kan u daarvoor contact opnemen met: [email protected]

Archeologisch proefsleuvenonderzoek ter hoogte van de Lammerdries in Olen (prov. Antwerpen)

Dit rapport werd ingediend bij het agentschap samen met een aantal afzonderlijke digitale bijlagen. Een aantal van deze bijlagen zijn niet inbegrepen in dit pdf document en zijn niet online beschikbaar. Sommige bijlagen (grondplannen, fotos, spoorbeschrijvingen, enz.) kunnen van belang zijn voor een betere lezing en interpretatie van dit rapport. Indien u deze bijlagen wenst te raadplegen kan u daarvoor contact opnemen met: [email protected]