On the Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces
arXiv:math/9804143 · doi:10.1016/S0393-0440(98)00048-5
Abstract
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).
25 pages, Latex