Balanced coalgebroids.
Berezin-Weyl quantization for Cartan motion groups
We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].
Bethe ansatz solutions of the Bose-Hubbard dimer.
Bianchi identities, Yang-Mills and Higgs field produced on -deformed bundle.
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.
Binary operations in classical and quantum mechanics
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply properties which are usually additionally required.
bm-independence and central limit theorems associated with symmetric cones
We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.
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.
Brisure de symétrie spontanée et géométrie du point de vue spectral