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  • 1.
    Arnlind, Joakim
    et al.
    Albert Einstein Institute, Golm, Germany..
    Silvestrov, Sergei
    Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
    Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems :: July 21-25 2008, Lorentz Center, Leiden, the Netherlands, satellite conference of the fifth European Congress of Mathematics, American Mathematical Society (AMS), 2009, 503, p. 1-25Chapter in book (Refereed)
    Abstract [en]

    Several classes of *-algebras associated to teh action of an affine transformation are considered, and an investigation of the interplay between the different classes is initiated. Connections are established that relate representations of *-algebras, geometry of algebraic surfaces, dynamics of affine transformations, graphs and algebras coming from a quantization procedure of Poisson structures. In particular, algebras related to surgaced being inverse images of fourth order polynomials (in ) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.

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