Noncommutative Zariski geometries and their classical limit
Confluentes Mathematici, Volume 2 (2010) no. 2, pp. 265-291.

We undertake a case study of two series of nonclassical Zariski geometries and show that these geometries can be realised as representations of certain noncommutative C*-algebras and introduce a natural limit construction which for each of the two series produces a classical U(1)-gauge field over a two-dimensional Riemann surface.

Published online:
DOI: 10.1142/S1793744210000181
Boris Zilber 1

1
@article{CML_2010__2_2_265_0,
     author = {Boris Zilber},
     title = {Noncommutative {Zariski} geometries and their classical limit},
     journal = {Confluentes Mathematici},
     pages = {265--291},
     publisher = {World Scientific Publishing Co Pte Ltd},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.1142/S1793744210000181},
     language = {en},
     url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744210000181/}
}
TY  - JOUR
AU  - Boris Zilber
TI  - Noncommutative Zariski geometries and their classical limit
JO  - Confluentes Mathematici
PY  - 2010
SP  - 265
EP  - 291
VL  - 2
IS  - 2
PB  - World Scientific Publishing Co Pte Ltd
UR  - https://cml.centre-mersenne.org/articles/10.1142/S1793744210000181/
DO  - 10.1142/S1793744210000181
LA  - en
ID  - CML_2010__2_2_265_0
ER  - 
%0 Journal Article
%A Boris Zilber
%T Noncommutative Zariski geometries and their classical limit
%J Confluentes Mathematici
%D 2010
%P 265-291
%V 2
%N 2
%I World Scientific Publishing Co Pte Ltd
%U https://cml.centre-mersenne.org/articles/10.1142/S1793744210000181/
%R 10.1142/S1793744210000181
%G en
%F CML_2010__2_2_265_0
Boris Zilber. Noncommutative Zariski geometries and their classical limit. Confluentes Mathematici, Volume 2 (2010) no. 2, pp. 265-291. doi : 10.1142/S1793744210000181. https://cml.centre-mersenne.org/articles/10.1142/S1793744210000181/

[1] B. A. Dubrovin , A. T. Fomenko and S. P. Novikov , Modern Geometry: Methods and Applications ( Springer-Verlag , 1990 ) .

[2] D. Evans, J. Inst. Math. Jussieu 7, 735 (2008), DOI: 10.1017/S1474748008000200.

[3] E. Hrushovski and B. Zilber, J. Amer. Math. Soc. 9, 1 (1996), DOI: 10.1090/S0894-0347-96-00180-4.

[4] A. I. Mal’tsev, Mat. Sb. 28, 567 (1951).

[5] G. Svetlichny, Preparation for gauge theory , arXiv:math-ph/9902027v1 .

[6] B. Zilber , Zariski Geometries , LMS Lecture Notes Series 360 ( Cambridge Univ. Press , 2010 ) .

[7] B. Zilber, Model Theory with Applications to Algebra and Analysis I, LMS Lect Notes 350, eds. H. D. Macpherson, A. Pillay and A. J. Wilkie (Cambridge Univ. Press, 2008) pp. 293–326.

Cited by Sources: