Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

Hopf Structures on Standard Young Tableaux

We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics. In this paper K is a field of characteristic zero and all vector spaces are over K. A K[S]-module is a collection of K[Sr]-modules of the symmetric groups Sr. A H(q)-module is a collect...

On the cyclic Homology of multiplier Hopf algebras

In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...

ar X iv : h ep - t h / 04 09 01 2 v 1 1 S ep 2 00 4 Construction of θ - Poincaré Algebras and their Invariants on M θ

In the present paper we construct deformations of the Poincaré algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate ansatz for the deformed Lorentz generator. They turn out to be Hopf algebras of quantum universal enveloping algebra type with nontrivial antipodes. In order ...

Drinfeld-hecke Algebras over Cocommutative Algebras

If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra SymV with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have been deformed by Drinfel’d and more recently, Crawley-Boevey and Holland, Etingof and Ginzburg (and Gan), and others. These algebras include symplectic reflection algebras and infi...

On the Coderivations of Some Hopf Algebras