Marija Dimitrijevic, Julius Wess
Deformed Bialgebra of Diffeomorphisms
Preprint series: ESI preprints

MSC:

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

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

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

PACS: 02.40.Gh,02.20.Uw
Abstract: The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates
is represented by differential operators on noncommutative spaces. The algebra remains unchanged,
the comultiplication however is deformed, that way we have found a deformed bialgebra of diffeomorphisms.
Scalar, vector and tensor fields are defined with appropriate transformation laws under the
deformed algebra and a differential calculus is developed. For pedagogical reasons the formalism is
developed for the $\theta$-deformed space as it is the best known example of deformed spaces.

Keywords: deformed spaces, derivatives, deformed diffeomorphisms