20 citations · 102 across the 71 of their papers we have counts for
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math.NT2016
Elliptic curves and continued fractions
Igor V. Nikolaev
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of ellipt…
math.AG2016
On tea, donuts and non-commutative geometry
Igor Nikolaev
As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theor…
math.OA2016★ 2 cited
Cluster C*-algebras and knot polynomials
Igor Nikolaev
We construct a representation of the braid groups in a cluster C*-algebra coming from a triangulation of the Riemann surface S with one or two cusps. It is shown that the Laurent p…