The Noncommutative Inhomogeneous Hopf Algebra

arXivq-alg/9705005MaRDI QIDQ6502339

M. Lagraa, Nabila Touhami

Abstract: From the bicovariant first order differential calculus on inhomogeneous Hopf algebra $calB$ we construct the set of right-invariant Maurer-Cartan one-forms considered as a right-invariant basis of a bicovariant $calB$-bimodule over which we develop the Woronowicz's general theory of differential calculus on quantum groups. In this formalism, we introduce suitable functionals on $calB$ 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 $calB$ and translations are controled by different R-matrices satisfying nontrivial characteristic equations.

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