arXiv subjects

Nurlan M. Sadykov

Publications and source records attributed to Nurlan M. Sadykov.

4 recordsLinked to original sources

arXiv2018

Hexagon cohomologies and polynomial TQFT actions

Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call `polynomial hexagon cohomologies'. Based on this, topological quantum field theories are proposed with polynomial `discrete Lagrangian densities' taking values in finite fields. First calculations of the resulting manifold invariants, arising from polynomial cocycles of degree three and in characteristic two, show their nontriviality.

math-ph↗

arXiv2015

Two-color solutions of set-theoretic tetrahedron equation and their cohomologies

All solutions of the set-theoretic constant tetrahedron equation with two colors are found, and some of their properties are analyzed. The list includes 406 solutions - we call them R-operators, - most of which are degenerate (non-bijective). Then, we calculate the 3-cohomologies for our R-operators, and discuss the applicability of our results to 3-dimensional statistical physics.

math.QA↗

arXiv2013

Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3

We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables on its five 3-faces. We show that there exists a large family of such relations; the problem is in finding their algebraic-topologically meaningful parameterization. We solve this problem in part, providing two nicely parameterized subfamilies of such relations. For the second of them, we further investigate the nature of some of its parameters: they turn out to correspond to an exotic analogue of middle homologies. In passing, we also provide the 2-4 Pachner move relation for this second case.

math.QA↗

arXiv2013

Pentagon Relations in Direct Sums and Grassmann Algebras

We construct vast families of orthogonal operators obeying pentagon relation in a direct sum of three n-dimensional vector spaces. As a consequence, we obtain pentagon relations in Grassmann algebras, making a far reaching generalization of exotic Reidemeister torsions.

math-ph↗