The Noncommutative Inhomogeneous Hopf Algebra
Abstract
From the bicovariant first order differential calculus on inhomogeneous Hopf algebra ${\cal B}$ we construct the set of rightinvariant MaurerCartan oneforms considered as a rightinvariant 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 Rmatrices satisfying nontrivial characteristic equations.
 Publication:

eprint arXiv:qalg/9705005
 Pub Date:
 May 1997
 DOI:
 10.48550/arXiv.qalg/9705005
 arXiv:
 arXiv:qalg/9705005
 Bibcode:
 1997q.alg.....5005L
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 25 pages, TeX, no figures. A section concerning the consistency conditions between the different functionals and the inhomogeneous commutation rules is added. Some references are also added