1995/07/20 by Mico Durdevic, Mićo Đurđević
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.QA #q-alg
paper · pdf · doi:10.1007/bf02099507
64 pages, AMS-LaTeX, To appear in CMP
arxiv created 1995/07/20 · openalex publication_date 1996/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential forms on the base manifold with an appropriate differential calculus on the structure quantum group. Relations between the calculus on the group and the calculus on the bundle are investigated. A concept of (pseudo)tensoriality is formulated. The formalism of connections is developed. In particular, operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. Generalizations of the first structure equation and of the Bianchi identity are found. Illustrative examples are presented.