1998/01/07 by Shahn Majid, S. Majid
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #math.QA
paper · pdf · doi:10.1016/s0393-0440(98)00016-3
36 pages latex with epsf (two figures, not critical)
arxiv created 1998/01/07 · openalex publication_date 1998/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group M(A) associated to an algebra A and its various quotients. Explicit formulae are introduced for this construction, as well as dual quasitriangular and braided R-matrix versions. Among the examples, we construct the q-diffeomorphisms of the quantum plane yx=qxy, and recover the quantum matrices Mq(2) as those respecting its braided group addition law.