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May 2014 Invariants of Stationary AF-Algebras and Torsion Subgroups of Elliptic Curves with Complex Multiplication
Igor Nikolaev
Missouri J. Math. Sci. 26(1): 23-32 (May 2014). DOI: 10.35834/mjms/1404997106

Abstract

Let $G_A$ be an $AF$-algebra given by a periodic Bratteli diagram with the incidence matrix $A\in GL(n, {\Bbb Z})$. For a given polynomial $p(x)\in {\Bbb Z}[x]$ we assign to $G_A$ a finite abelian group $Ab_{p(x)}(G_A)={\Bbb Z}^n/p(A){\Bbb Z}^n$. It is shown that if $p(0)=\pm 1$ and ${\Bbb Z}[x]/\langle p(x)\rangle$ is a principal ideal domain, then $Ab_{p(x)}(G_A)$ is an invariant of the strong stable isomorphism class of $G_A$. For $n=2$ and $p(x)=x-1$ we conjecture a formula linking values of the invariant and torsion subgroup of elliptic curves with complex multiplication.

Citation

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Igor Nikolaev. "Invariants of Stationary AF-Algebras and Torsion Subgroups of Elliptic Curves with Complex Multiplication." Missouri J. Math. Sci. 26 (1) 23 - 32, May 2014. https://doi.org/10.35834/mjms/1404997106

Information

Published: May 2014
First available in Project Euclid: 10 July 2014

zbMATH: 1364.11113
MathSciNet: MR3229946
Digital Object Identifier: 10.35834/mjms/1404997106

Subjects:
Primary: 11G15
Secondary: 46L85

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.26 • No. 1 • May 2014
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