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Helena Albuquerque (Coimbra, Portugal)

Quasialgebras and Matrices

Abstract. We briefly review the common approach of Cayley Algebras and Clifford Algebras as quasialgebras and we present some examples of deformed group algebras of matrices related to "quasilinear" algebra.

Boujemaa Agrebaoui (Sfax, Tunisia)

Simple multiplicative Hom-Lie algebras and their representations.

Azouz Awane (Casablanca, Morocco)

Geometrie symplectique vectorielle polarisee

Ali Baklouti (Sfax, Tunisia)

Representations monomiales a multiplicites de type discret des groupes de Lie resolubles exponentiels

Amir Baklouti (Umm Al-Qura, Saudi Arabia)

Caracterisations des systemes triples de Lie semi-simples

Mabrouk Ben Ammar (Sfax, Tunisia)

Cohomology of sl(2) acting on the space of n-ary differential operators on R

Chengming Bai (Nankai U., China)

Deformations and their controlling cohomologies of O-operators

Abstract. We establish a deformation theory of a kind of linear operators, namely, O-operators in consistence with the general principles of deformation theories. On one hand, there is a suitable differential graded Lie algebra whose Maurer-Cartan elements characterize O-operators and their deformations. On the other hand, there is an analogue of the Andr\'e-Quillen cohomology which controls the deformations of O-operators. Infinitesimal deformations of O-operators are studied and applications are given to deformations of skew-symmetric r-matrices for the classical Yang-Baxter equation. This is a joint work with Li Guo, Yunhe Sheng and Rong Tang.

Ismail Benali (Casablanca, Morocco)

Quelques proprietes metriques des varietes symplectiques vectorielles polarisees

Said Benayadi (Metz, France)

Leibniz algebras with invariant bilinear forms

Abstract. In the case of Lie algebras, the left (resp. right) invariance of bilinear forms is equivalent to the invariance (or associativity) of these forms. However, it is not the case for Leibniz algebras. In this talk, we will give some results on the structures of Leibniz algebras which are provided with symmetric non-degenerate bilinear forms which are either left (resp; right) invariant or associative.

Rabeya Basu (Pune, India)

On Quillen-Suslin Theory

Abstract.  In this talk we shall discuss Quillen--Suslin's local-global principle for the "classical type" groups; in particular an analogue of this principle for the transvection subgroups of the general quadratic (Bak's unitary) groups. As an application we will revisit the result of Bak--Petrov--Tang  on injective stabilization for the K_1-functor of the general quadratic groups.

Mohamed Boucetta (Marrakech, Morocco)

Contravariant pseudo-Hessian structures

Abstract. We introduce a natural generalization of pseudo-Hessian manifolds, we call them contravariant pseudo-Hessian Manifolds. Contravariant pseudo-Hessian manifolds have many similarities with Poisson manifolds. We explore these similarities which, among others, leads to a powerful machinery to build examples of non trivial pseudo-Hessian structures. Namely, we will show that given a finite dimensional commutative and associative algebra (A; .), the orbits of the action  F of (A; +) on A^* given by F(a; mu) = exp(L^*_a)(mu) are pseudo-Hessian manifolds, where L_a(b) = a.b. We illustrate this result by considering many examples of associative commutative algebras and show that the pseudo-Hessian manifolds obtained are very interesting.

Abdelhamid Boussejra (Kenitra, Morocco)

Poisson transform on homogeneous line bundles over bounded symmetric domains.

Nizar Benfraj (Sfax, Tunisia)

Cohomology of some Lie superalgebras acting on some modules and deformations

Abstract. Over the (1,2)-dimensional real superspace, we compute the cohomology space of the affine Lie superalgebra aff(2) with coefficient in a large class of aff(2)-modules M.

We apply our results to the module M=\mathfrak{F}^2_\lambda of weight densities and the module M =\mathfrak{D}^2_{\lambda,\mu} of linear differential operators acting on a superspace of weighted densities. We study non-trivial deformations of the natural action of the Lie superalgebra aff(2) on the direct sum of the superspaces of weighted densities. We also compute the first differential osp(1|2)-relative cohomology of  the Lie superalgebra K(1) of contact vector fields on R^{1|1} with coefficients in D^1_{\lambda,\mu;\nu}:=Hom_{diff}(F^1_{\lambda}\otimes\F^1_{\mu},F}^1_{\nu}).

Souhaila El Amine (Casablanca, Morocco)

Varietes de Poisson  vectorielles polarisees

Yael Fregier (Lens, France)

Tba

Ashis Gupta (Vivekananda University, India)

Ring and Module-theoretic aspects of quantum polynomials

Abstract. The Gelfand​-Kirillov dimension (GK dimension) is an important tool in the study of non-commutative algebras and their modules. We will explain what this dimension is how it is related to the other dimensional invariants for rings. We will present a few theorems on the GK dimensions some simple rings and their modules.  We will also present a few theorems for the simple modules of quantum torus.

Benedikt Hurle (Mulhouse, France)

Alpha-type Cohomology and Deformations of Hom-algebras

Abstract. Hom-Lie algebras where first introduced in the study of q-deformations of Lie algebras appearing in physics. Here the Jacobi identity is twisted by a morphism called structure map. Later other type of Hom-algebras, e.g. Hom-associative algebras, have been defined and studied. In this I want to define a generalization of the Hochschild cohomology for associative algebras to the Hom setting. We call this new cohomology alpha-type Hochschild cohomology. It can be used to study  formal deformations in the sense of Gerstenhaber, where the multiplication and the structure map are deformed. I will  also briefly discuss an alpha-type cohomology for Hom-Lie algebras.

Natalia Iyudu (Edinburg, Scotland)

Koszulity of potential algebras and operadic homology

Abstract. I will describe methods based in particular on Groebner bases theory which  allowed us to prove Koszulity, Calabi-Yau, PBW type properties, calculate Hilbert series, etc. for such classes of potential algebras as Sklyanin algebras,  contraction algebras, homology of moduli spaces of pointed curves M_{0,6} of genus zero. I will also mention methods which allowed us  to calculate homologies of some interesting monomial operads.

Camille Laurent-Gengoux (Metz, France)

An invitation to singular foliations

Abstract. There has been a recent surge of interest for singular foliations, coming from holomorphic, Poisson and non-commutative geometry. I will try to explain what are the "hidden structures" (groupoids, Lie-infinity algebroids) of a singular foliation and give a few open questions on the matter.

Natalia Makarenko (Mulhouse, France)

Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebra

Abstract. I will speak about the recent result that almost nilpotency of the fixed-point subalgebra in an associative algebra admitting a solvable finite group of automorphisms, implies almost nilpotency of the algebra itself.

Alberto Medina (Montpelier, France)

Transformations des varietes affines plates

Abstract. Cet expose a pour objectif de vous presenter certaines avancees que nous avons pu faire dans notre tentative de comprehension de la geometrie affine plate. En voici quelques unes :

1, Donner une caracterisation des varietes reelles affines plates  paracompactes, en termes de la forme de la connexion et de la forme fondamentale du fibré P=L(M) des reperes lineaires de la variete.

2, Mettre en evidence la existence d'un groupe de Lie connexe et simplement connexe, muni d'une structure affine plate bi-invariante dont l'algebre de Lie contient l'algebre de Lie des transformations affines infinitesimales completes, d'une variete affine plate.

3, Associer, d'une maniere naturelle, a une algebre symetrique à gauche reelle de dimension finie A, une algebre associative dont l'algebre des commutateurs contient l'algebre des commutateurs de A.

Cette etude a ete faite, en partie, en collaboration avec une petite equipe de géométrie differentielle que nous avons pu monter en Colombie.

Anita Naolekar (Bangalore, India)

Versal Deformation Theory of Algebras over a Quadratic Operad

Abstract: In this talk, we shall discuss deformation theory of algebras over a quadratic operad, where the parameter space is a complete local algebra. Time permits, we shall see an example of a distinguished deformation, called versal deformation, which induces all other deformations of the given algebra.This talk is based on a joint work by G. Mukherjee and A. Fialowski.

Rosa Navarro (Estremadura, Spain)

Low-dimensional filiform Lie algebras

Abstract. Throught this work the author does an analogue for superalgebras of the work "Low-dimensional filiform Lie algebras" done by  Yu khakimdjanov in 1998. In particular,  the present work is regarding filiform Lie superalgebras which is an important type of nilpotent Lie superalgebras. In general, classifying nilpotent Lie superalgebras is at present an open and unsolved problem. Thus, with the present work we contribute to the resolution of this wide problem by classifying filiform Lie superalgebras of low dimensions, in particular less or equal to 7. Furthermore we stablish a method that could be applied to obtain similar results for higher dimensions. The aforementioned method mainly consists in using infinitesimal deformations of the model filiform Lie superalgebra.

Natalia Pacheco Rego (IPCA, Barcelos, Portugal)

Universal alpha -central extensions, non abelian tensor product and unicentrality of Hom-Leibniz n-algebras

Elisabeth Remm (Mulhouse, France)

Etude geometrique des orbites coadjointes d'une algebre de Lie.

Peter Schauenburg (Dijon, France)

Invariants for modular fusion categories

Abstract. Fusion categories, and, much more specifically, modular fusion categories, are abstract abelian categories with a tensor product subject to lengthy axiomatic requirements that force them to behave similarly to (but then, with the "last" axiom for modular categories, distinctly differently from) the ordinary representation categories of finite groups. Understanding such categories can be understood as a purely algebraic problem, but the interest in these structures comes from their appearance in various contexts of mathematical physics. A modular category allows to define a topological quantum field theory, in particular a system of algebraic invariants of three-manifolds and knots and links. The modular data of a modular catgegory are instances of these invariants. Perhaps due to the important role that the modular data play in the structure theory of modular categories and in some links to mathematical physics, the question as to whether the modular data are a complete invariant for modular categories was for some time seriously considered; however, we recently found counterexamples to this conjecture. The counterexamples raise the natural question whether numerical invariants akin to the modular data can be found (and used in practice) that can distinguish categories sharing the same modular data. For example, the S-matrix which is part of the modular data is the invariant of the Hopf link in the TQFT defined by the category; can the value of the invariant on other links be used to tell categories apart that give the same value of their invariants on the Hopf link? (The talk is based on work with my PhD students Michaël Mignard and AJinkya Kulkarni.)

Arvid Siqveland (University College of Southeast Norway)

Moduli of n-Lie algebras

Abstract. We will start by giving the definition and results of noncommutative deformation theory needed for applications in geometry. These results are used to define noncommutative schemes as moduli for their simple modules, and we prove how this gives orbit spaces X/G for reductive group-actions on schemes X. Following this discussion, we give the definition of n-Lie algebras, and prove that they are parametrized by a noncommutative scheme that is a quotient of an affine scheme by a linear group-action. Finally, we will give the definition of a dynamic action on a noncommutative scheme by introducing its phase space, and prove that this gives invariants on the moduli of n-Lie algebras.

Ahmad Tayyar (Jerrash U.,  Jordan)

Construction d’un système de géodésie pour la détermination du plus court chemin.

Blas Torrecillas (Almeria Spain)

Cleft wreath algebras

Abstract.  We study cleft wreath algebras and its relation with cleft cowreath associated to Galois theory of these structures. We apply this theory to different situations: crossed products for coalgebras, generalized crossed products and quiasi-Hopf bimodules.

(This is a joint work with D. Bulacu)

David Towers (Lancaster, UK)

The nilpotent length of a solvable Lie algebra

Abstract. In this talk we introduce the concept of the nilpotent length of a finite-dimensional solvable Lie algebra and use it to investigate solvable Lie algebras of nilpotent length k, of nilpotent length <= k, and extreme Lie algebras, which have the property that their nilpotent length is equal to the number of conjugacy classes of maximal subalgebras. We will also look at Lie algebras with nilpotent length greater than that of each of their subalgebras.

Yinhuo Zhang (Hasselt, Belgium)

On the center of the quantized enveloping algebra of a simple Lie algebra