Anyonic Groups
Asymmetric twin representation: the transfer matrix symmetry.
Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple -Manifolds
Automorphismes de certains completés du corps de Weyl quantique.
Automorphisms of . (Automorphismes de .)
Bases canoniques et applications
Bases des représentations des groupes simples complexes
Bialgebra structures on a real semisimple Lie algebra.
Bicovariant differential calculi and cross products on braided Hopf algebras
In a braided monoidal category C we consider Hopf bimodules and crossed modules over a braided Hopf algebra H. We show that both categories are equivalent. It is discussed that the category of Hopf bimodule bialgebras coincides up to isomorphism with the category of bialgebra projections over H. Using these results we generalize the Radford-Majid criterion and show that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. In specific braided monoidal...
Bicrossproduct Hopf quasigroups
We recall the notion of Hopf quasigroups introduced previously by the authors. We construct a bicrossproduct Hopf quasigroup from every group with a finite subgroup and IP quasigroup transversal subject to certain conditions. We identify the octonions quasigroup as transversal in an order 128 group with subgroup and hence obtain a Hopf quasigroup as a particular case of our construction.
Braided Groups
Braided modules and reflection equations
We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.
Calculations with the Temperley - Lieb algebra.
Category for quantum groups
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for and for finite dimensional -modules we are able to determine...
Cellular algebras.
Central extensions of three dimensional Artin-Schelter regular algebras.
Classification of the simple modules of the quantum Weyl algebra and the quantum plane
Classification theorem on irreducible representations of the -deformed algebra .
Commutator representations of covariant differential calculi
Complexes de Koszul quantiques
Nous construisons des généralisations des complexes de Koszul, associées à des symétries vérifiant l’équation de Yang-Baxter. Certains de ces complexes sont acycliques et permettent de calculer l’homologie de Hochschild et cyclique de déformations quantiques d’algèbres symétriques et extérieures. Nous donnons des résultats précis pour l’espace affine quantique multiparamétré. Il est également possible de définir des complexes de Koszul pour des algèbres enveloppantes et de Sridharan d’algèbres de...