On the Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces

Details On the Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces On the Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces

1998-04-30

arxiv.org/abs/math/9804143v1

Mathematics

Quantum Algebra

25 pages, Latex

Scientific paper

10.1016/S0393-0440(98)00048-5

Let A be a coquasitriangular Hopf algebra and X the subalgebra of A generated by a row of a matrix corepresentation u or by a row of u and a row of the contragredient representation u^c. In the paper left-covariant first order differential calculi on the quantum group A are constructed and the corresponding induced calculi on the left quantum space X are described. The main tool for these constructions are the L-functionals associated with u. The results are applied to the quantum homogeneous space GL_q(N)/GL_q(N-1).

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