Related papers: 6J Symbols Duality Relations

We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras ${\cal H}^c$ that we recently introduced. We show that if the standard Hopf (super)algebras ${\cal H}_q$ that are the building blocks of…

The properties of Hopf star operations and twisted Hopf stars operations on quantum groups are discussed in relation with the theory of representations (star representations). Invariant Hermitian sesquilinear forms (scalar products) on…

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…

Let G be the group of all formal power series starting with x with coefficients in a field k of zero characteristic (with the composition product), and let F[G] be its function algebra. C. Brouder and A. Frabetti introduced a…

Using equivalences of categories we provide isomorphisms between the Brauer groups of different Hopf algebras. As an example, we show that when k is a field of characteristic different from 2 the Brauer groups BC(k,H_4,r_t) for every dual…

A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…

We answer a question posed by Fielder in [1] concerning two notions of crossing number for algebraic knots $K$ under Hopf fibration, one topological, denoted $h(K)$, the other coming from the realization of such knots around complex…

We study the self-dual Hopf algebra $\h\_{\SP}$ of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from $\h\_{\SP}$ to to the Hopf algebra of free quasi-symmetric functions $\FQSym$ given by linear…

A pre-subgroup of a multiplicative unitary $V$ on a finite dimensionnal Hilbert space $H$ is a vector line $L$ in $H$ such that $V(L\otimes L)=L\otimes L$. We show that there are finitely many pre-subgroups, give a Lagrange theorem and…

We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of…

We formulate a conjecture, stating that the algebra of $n$ pairs of deformed Bose creation and annihilation operators is a factor-algebra of $U_q[osp(1/2n)]$, considered as a Hopf algebra, and prove it for $n=2$ case. To this end we show…

Multiplier Hopf algebroids are algebraic versions of quantum groupoids that generalize Hopf algebroids to the non-unital case and weak (multiplier) Hopf algebras to non-separable base algebras. The main structure maps of a multiplier Hopf…

The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of…

The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical value of parameters the equilibrium with two pairs of double…

A 3-manifold is called \emph{SU(2)}-abelian if every SU(2)-representation of its fundamental group has abelian image. We classify, in terms of the Seifert coefficients, SU(2)-abelian 3-manifolds among the family of graph manifolds obtained…

We construct a Hopf algebra cocycle in the Yangian double $DY(SL_{2})$, conjugating Drinfeld's coproduct to the usual one. To do that, we factorize the twist between two ``opposite'' versions of Drinfeld's coproduct, introduced in earlier…

A fundamental feature of quantum groups is that many come in pairs of mutually dual objects, like finite-dimensional Hopf algebras and their duals, or quantisations of function algebras and of universal enveloping algebras of Poisson-Lie…

Let $(A,\Delta)$ be a finite-dimensional Hopf algebra. The linear dual $B$ of $A$ is again a finite-dimensional Hopf algebra. The duality is given by an element $V\in B\otimes A$, defined by $\langle V,a\otimes b\rangle=\langle a,b\rangle$…

We show that su(2) rational and trigonometric Gaudin models, or in other words, generalised coupled angular momenta systems, have singularities that undergo Hamiltonian Hopf bifurcations. In particular, we find a normal form for the…