Affine transformation crossed product like algebras and noncommutative surfaces

2009/03/11 by Joakim Arnlind, Arnlind, Joakim, Sergei Silvestrov +1
Mathematics · Physics and Astronomy · #16G99 #16S35 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math-ph #math.MP #math.QA #math.RT #msc:16G99 #msc:16S35

paper · pdf · doi:10.48550/arxiv.0903.1925

arxiv created 2009/03/11 · arxiv updated 2009/12/01

Abstract

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras 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 surfaces being inverse images of fourth order polynomials (in R³) 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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