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The inhomogeneous quantum groups from differential calculi with classical dimension. (English) Zbl 0982.17007
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 [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.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W35 Ring-theoretic aspects of quantum groups (MSC2000)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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