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  Affine transformation crossed product like algebras and noncommutative surfaces

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0012-BD2D-7 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-8060-D
Genre: Book Chapter

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0903.1925 (Preprint), 583KB
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 Creators:
Arnlind, Joakim1, Author           
Silvestrov, Sergei, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_persistent22              

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Free keywords: Mathematical Physics, math-ph,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP,Mathematics, Quantum Algebra, math.QA,Mathematics, Representation Theory, math.RT,
 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.

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 Dates: 2009-03-112009
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 0903.1925
 Degree: -

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Title: Operator Structures and Dynamical Systems (Contemporary Mathematics)
Source Genre: Book
 Creator(s):
de Jeu, Marcel, Editor
Silvestrov, Sergei, Editor
Skau, Christian, Editor
Tomiyama, Jun, Editor
Affiliations:
-
Publ. Info: American Mathematical Society
Pages: - Volume / Issue: 503 Sequence Number: - Start / End Page: 1 - 26 Identifier: ISBN: 978-0-8218-4747-3