K-theory of Jones polynomials
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 Jones polynomials is studied.
math.OA↗
arXiv subjects
Andrey Glubokov
Publications and source records attributed to Andrey Glubokov.
Subfactors and Hecke groups
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 notion of a cluster C*-algebra.
math.OA↗
Ideals on the Quantum Plane's jet space
The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the prime spectrum of these rings.
math.QA↗