The quantum Cartan algebra associated to a bicovariant differential calculus

preprint2010arXivOpen access

Abstract

We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of the Hopf algebra associated to the 4D+4D_+ differential calculus on SUq(2)SU_q(2) is described.

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