Covariant differential complexes on quantum linear groups

Details Covariant differential complexes on quantum linear groups Covariant differential complexes on quantum linear groups

1993-11-19

arxiv.org/abs/hep-th/9311112v1

J.Phys. A28 (1995) 2227-2246

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1088/0305-4470/28/8/015

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all monomials of these forms possess the unique ordering. For the obtained external algebras we define the exterior derivative possessing the usual nilpotence condition, and the generally deformed version of Leibniz rules. The status of the known examples of GL_q(N)-differential calculi in the proposed classification scheme, and the problems of SL_q(N)-reduction are discussed.

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