A generalised Hopf algebra for solitons.
A new rational free-fermion solution of the Yang-Baxter equation.
A note on coalgebra gauge theory
A generalisation of quantum principal bundles in which a quantum structure group is replaced by a coalgebra is proposed.
À propos du calcul différentiel sur les groupes quantiques
A -analogue of the centralizer construction and skew representations of the quantum affine algebra.
A -representation with no quantum symmetric algebra
We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.
Addendum to "Generalized radical rings, unknotted biquandles, and quantum groups" (Colloq. Math. 109 (2007), 85-100)
Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus
The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review.
An Analogue of the Classical Yang-Baxter Equation for General Algebraic Structures.
An idempotent for a Jordanian quantum complex sphere
A new Jordanian quantum complex 4-sphere together with an instanton-type idempotent is obtained as a suspension of the Jordanian quantum group .
An infinite torus braid yields a categorified Jones-Wenzl projector
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.
Anyonic Groups
Asymmetric twin representation: the transfer matrix symmetry.
Balanced coalgebroids.
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.
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.