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May 2018 Noncommutative geometry of rational elliptic curves
Igor V. Nikolaev
Ann. Funct. Anal. 9(2): 202-209 (May 2018). DOI: 10.1215/20088752-2017-0045

Abstract

We study an interplay between operator algebras and the geometry of rational elliptic curves. Namely, let OB be the Cuntz–Krieger algebra given by a square matrix B=(b1,1,b2,1), where b is an integer greater than or equal to 2. We prove that there exists a dense, self-adjoint subalgebra of OB which is isomorphic (modulo an ideal) to a twisted homogeneous coordinate ring of the rational elliptic curve E(Q)={(x,y,z)P2(C)y2z=x(xz)(xb2b+2z)}.

Citation

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Igor V. Nikolaev. "Noncommutative geometry of rational elliptic curves." Ann. Funct. Anal. 9 (2) 202 - 209, May 2018. https://doi.org/10.1215/20088752-2017-0045

Information

Received: 12 February 2017; Accepted: 20 April 2017; Published: May 2018
First available in Project Euclid: 11 December 2017

zbMATH: 06873697
MathSciNet: MR3795085
Digital Object Identifier: 10.1215/20088752-2017-0045

Subjects:
Primary: 46L85
Secondary: 14H52

Keywords: Cuntz–Krieger algebras , rational elliptic curves

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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