Abstract
We discuss examples of non-commutative spaces over non-archimedean fields. Those include non-commutative and quantum affinoid algebras, quantized K3 surfaces and quantized locally analytic p-adic groups. In the latter case we found a quantization of the Schneider–Teitelbaum algebra of locally analytic distributions by using the ideas of representation theory of quantized function algebras.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Bosch, U. Güntzer, R. Remmert, Non-archimedean analysis. Springer-Verlag, (1984).
V. Berkovich, Spectral theory and analytic geometry over non-archimedean fields. AMS Math. Surveys and Monographs, n. 33, 1990.
V. Berkovich, Etale cohomology for non-Archimedean analytic spaces, Publ. Math. IHES 78 (1993), 5–161.
V. Berkovich, Smooth p-adic analytic spaces are locally contractible, Inv. Math., 137 (1999), 1–84.
A. Connes, Non-commutative geometry, Academic Press, 1994.
V. Fock, A. Goncharov, Cluster ensembles, quantization and the dilogarithm, math.AG/0311245.
J. Fresnel, M. van der Put, Rigid analytic geometry and applications. Birkhauser, (2003).
M. Kontsevich, Y. Soibelman, Affine structures and non-archimedean analytic spaces, math.AG/0406564.
M. Kontsevich, Y. Soibelman, Homological mirror symmetry and torus fibrations, math.SG/0011041.
M. Kontsevich, A. Rosenberg, Non-commutative smooth spaces, math.AG/ 9812158.
L. Korogodsky, Y. Soibelman, Algebras of functions on quantum groups. I, Amer. Math. Soc., (1997).
Lapchik, personal communications, 2004–2005, see also www.allalapa.net
A. Rosenberg, Non-commutative algebraic geometry and representations of quantized algebras. Kluwer Academic Publishers, (1995).
A. Rosenberg, Y. Soibelman, Non-commutative analytic spaces, in preparation.
P. Schneider, J. Teitelbaum, Algebras of p-adic distributions and admissible representations, Invent. math. 153, 145–196 (2003).
Y. Soibelman, V. Vologodsky, Non-commutative compactifications and elliptic curves, math.AG/0205117, published in Int. Math.Res. Notes, 28 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Soibelman, Y. (2008). On Non-Commutative Analytic Spaces Over Non-Archimedean Fields. In: Homological Mirror Symmetry. Lecture Notes in Physics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68030-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-68030-7_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68029-1
Online ISBN: 978-3-540-68030-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)