arXiv subjects

N. Touhami

Publications and source records attributed to N. Touhami.

3 recordsLinked to original sources

arXiv2003

Fusion and exchange matrices for quantized sl(2) and associated q-special functions

The aim of this paper is to evaluate in terms of q-special functions the objects (intertwining map, fusion matrix, exchange matrix) related to the quantum dynamical Yang-Baxter equation (QDYBE) for infinite dimensional representations (Verma modules) of the quantized universal enveloping algebra of g=sl(2,C). This study is done in the framework of the exchange construction, which was initiated (for general semisimple g) by Etingof and Varchenko (math.QA/9801135} and surveyed by Etingof and Schiffmann (math.QA/9908064) and Etingof (math.QA/0207008). Special attention is paid to the shifted boundary introduced by Babelon, Bernard and Billey (q-alg/9511019) and to its coincidence (first observed by Rosengren) with Rosengren's generalized elements in U_q(sl(2)) for conjugation. The present paper extends in various aspects our earlier paper math.QA/0007086, which dealt with q=1.

math.QA↗

arXiv1997

The Noncommutative Inhomogeneous Hopf Algebra

From the bicovariant first order differential calculus on inhomogeneous Hopf algebra ${\cal B}$ we construct the set of right-invariant Maurer-Cartan one-forms considered as a right-invariant basis of a bicovariant ${\cal B}$-bimodule over which we develop the Woronowicz's general theory of differential calculus on quantum groups. In this formalism, we introduce suitable functionals on ${\cal B}$ which control the inhomogeneous commutation rules. In particular we find that the homogeneous part of commutation rules between the translations and those between the generators of the homogeneous part of ${\cal B}$ and translations are controled by different R-matrices satisfying nontrivial characteristic equations.

q-alg↗

arXiv1997

Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra

We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.

q-alg↗