20 citations · 102 across the 71 of their papers we have counts for
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Quantum arithmetic dynamics
Igor Nikolaev
We study dynamics of the Lattès maps in the complex plane in terms of the Cuntz-Krieger algebras associated to the endomorphisms of the non-commutative tori. In particular, it is s…
K-theory of Jones polynomials
Andrey Glubokov, Igor Nikolaev
We recover the Jones polynomials of knots and links from the K-theory of a cluster C*-algebra of the sphere with two cusps. In particular, an interplay between the Chebyshev and Jo…
Subfactors and Hecke groups
Andrey Glubokov, Igor Nikolaev
We study a relation between the Hecke groups and the index of subfactors in a von Neumann algebra. Such a problem was raised by V. F. R. Jones. We solve the problem using the notio…
Jones Index Theorem revisited
Andrey Yu. Glubokov, Igor V. Nikolaev
We prove the Jones Index Theorem using the K-theory of a cluster -algebra of the Riemann sphere with two boundary components.
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…
K-theory of cluster C*-algebras
Igor Nikolaev
It is proved that the K_0-group of a cluster C*-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture fo…