Combinatorics of $φ$-deformed stuffle Hopf algebras

Combinatorics of $\phi$-deformed stuffle Hopf algebras

In order to extend the Schützenberger’s factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the φ-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product. and in emphasizing the Lie elements as studied by Ree. In particular, we will give an effective construction of pair of bases in duality.

Combinatorics of / / / φ -

In order to extend the Schützenberger’s factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the φ-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product. and in emphasizing the Lie elements as studied by Ree. In particular, we will give an effective construction of pair of bases in duality.

The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf Uh;y(sl(2)) algebra

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf Uh;y(sl(2)) algebra. The corresponding universal Rh(y) matrix obeys a Gervais-Neveu-Felder equation associated with the Uh;y(sl(2)) algebra. For a class of representations, the dynamical Yang-Baxter equation may be expressed as a compatibility condition ...

Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Gree...

On the Coderivations of Some Hopf Algebras