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CONFLUENTES MATHEMATICI

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no. 2
Noncommutative Zariski geometries and their classical limit
Confluentes Mathematici, Tome 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.

Publié le :
DOI : 10.1142/S1793744210000181
Boris Zilber 1

1 
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Boris Zilber. Noncommutative Zariski geometries and their classical limit. Confluentes Mathematici, Tome 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.

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