Shahn Majid
Duality Principle and Braided Geometry
Preprint series: ESI preprints

MSC:

16W30 Coalgebras, bialgebras, Hopf algebras, See also {57T05,

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

Abstract: We give an overview of a new kind symmetry in physics which
exists between observables and states and which is made
possible by the language of Hopf algebras and quantum
geometry. It has been proposed by the author as a
feature of Planck scale physics. More recent work
includes corresponding results at the semiclassical level
of Poisson-Lie groups and at the level of
braided groups and braided geometry.
Keywords: quantum groups, noncommutative geometry, braided geometr y, integrable systems, Poisson structure, Mach principle, $\kappa$-deformation, q-deformation