Universal deformation formulae, symplectic Lie groups and symmetric spaces

Pierre Bieliavsky, Philippe Bonneau, Yoshiaki Maeda

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    We define a class of symplectic Lie groups associated with solvable symmetric spaces. We give a universal strict deformation formula for every proper action of such a group on a smooth manifold. We define a functional space where performing an asymptotic expansion of the nonformal deformed product in powers of the deformation parameter yields an associative formal star product on the symplectic Lie group at hand. The cochains of the star product are explicitly given (without recursion) in the two-dimensional case of the affine group ax + b. The latter differs from the Giaquinto-Zhang construction, as shown by analyzing the invariance groups. In a Hopf algebra context, the above formal star product is shown to be a smash product and a compatible coproduct is constructed.

    Original languageEnglish
    Pages (from-to)41-57
    Number of pages17
    JournalPacific Journal of Mathematics
    Volume230
    Issue number1
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Lie group actions
    • Symmetric space
    • Symplectic Lie group
    • Universal deformation formula

    ASJC Scopus subject areas

    • Mathematics(all)

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