Search results for " Representation."
showing 10 items of 791 documents
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.
Hom-Lie quadratic and Pinczon Algebras
2017
ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.
A note on the Lawrence-Krammer-Bigelow representation
2002
A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.
A Use Case of Data Integration in Food Production
2018
International audience; This paper presents a use case about knowledge representation and integration of data from different domains in food science. An ontology named PO 2 DG, the Process and Observation Ontology for the production of Dairy Gels, has been designed in order to provide a shared vocabulary for domain experts. The available data have been semantically structured using PO 2 DG and are stored in an RDF repository named PO 2 DG dataset. This use case identifies some of the challenges when dealing with a multi domain representation problem, gives some hints about possible solutions and suggests some further work.
Ontology-based Integration of Web Navigation for Dynamic User Profiling
2015
The development of technology for handling information on a Big Data-scale is a buzzing topic of current research. Indeed, improved techniques for knowledge discovery are crucial for scientific and economic exploitation of large-scale raw data. In research collaboration with an industrial actor, we explore the applicability of ontology-based knowledge extraction and representation for today's biggest source of large-scale data, the Web. The goal is to develop a profiling application, based on the implicit information that every user leaves while navigating the online, with the goal to identify and model preferences and interests in a detailed user profile. This includes the identification o…
Semantic Mappings in Description Logics for Spatio-temporal Database Schema Integration
2005
International audience; The interoperability problem arises in heterogeneous systems where different data sources coexist and there is a need for meaningful information sharing. One of the most representive realms of diversity of data representation is the spatio-temporal domain. Spatio-temporal data are most often described according to multiple and greatly diverse perceptions or viewpoints, using different terms and with heterogeneous levels of detail. Reconciling this heterogeneity to build a fully integrated database is known to be a complex and currently unresolved problem, and few formal approaches exist for the integration of spatio-temporal databases. The paper discusses the interope…
New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology
2007
We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.
Nouveaux aliments à base de légumineuses : les consommateurs sont-ils prêts ?
2018
National audience
The hidden face of expertise! Representations and descriptions of wines by different groups of experts in a vineyard in full evolution : the Beaujola…
2022
The Beaujolais vineyard is today in full evolution thanks to a policy of upgrading and moving upmarket. This evolution leads to the development of new mentions within the vineyard. This evolution impacts the Beaujolais wines but also the wine experts who are in the heart of making, selling and promoting these wines. Wine expertise has been studied extensively over the past twenty years. Most studies have focused on experts as a unified group versus novices to understand the effect of expertise on the knowledge and abilities of experts. However, it appears that within this unity, there are several types of experts with different backgrounds, knowledge, experiences, and professions: wine make…
La catégorisation d'un exogroupe à travers une tâche d'association de mots
2001
International audience