an:01492154
Zbl 0982.17007
Lagraa, M.; Touhami, N.
The inhomogeneous quantum groups from differential calculi with classical dimension
EN
J. Math. Phys. 40, No. 11, 6052-6070 (1999).
00068324
1999
j
17B37 16W35 81R50
Woronowicz theory; bicovariant first-order differential calculus; inhomogeneous Hopf algebra; right-invariant Maurer-Cartan one-forms; quantum groups; commutation rules
Authors' summary: From the bicovariant first-order differential calculus on inhomogeneous Hopf algebra \({\mathcal B}\) the authors construct the set of right-invariant Maurer-Cartan one-forms considered as a right-invariant basis of a bicovariant \({\mathcal B}\)-bimodule over which they develop the Woronowicz general theory of differential calculus on quantum groups [\textit{S. L. Woronowicz}, Commun. Math. Phys. 122, 125-170 (1989; Zbl 0751.58042)]. In this formalism, they introduce suitable functionals on \({\mathcal B}\) which control the inhomogeneous commutation rules. In particular, they find that the homogeneous part of commutation rules between the translations and those between the generators of the homogeneous part of \({\mathcal B}\) and translations are controlled by different \(R\)-matrices satisfying characteristic equations.
Zbl 0751.58042