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Book Chapter

Affine transformation crossed product like algebras and noncommutative surfaces

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons4309

Arnlind,  Joakim
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

0903.1925
(Preprint), 583KB

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Citation

Arnlind, J., & Silvestrov, S. (2009). Affine transformation crossed product like algebras and noncommutative surfaces. In M. de Jeu, S. Silvestrov, C. Skau, & J. Tomiyama (Eds.), Operator Structures and Dynamical Systems (Contemporary Mathematics) (pp. 1-26). American Mathematical Society.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-BD2D-7
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 R^3) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.