Arpan Kanrar

collaborators

5 papers

math.GR2025

On Modular maximal-cyclic braces

Arpan Das, Arpan Kanrar

Inspired by a conjecture by Guarnieri and Vendramin concerning the number of braces with a generalized quaternion adjoint group, many researchers have studied braces whose adjoint…

math.QA2025

On indecomposable involutive solutions to the Yang-Baxter equation whose squaring map is a $p$ -cycle

Marco Castelli, Arpan Kanrar

The pioneering work of Rump, which proved Gateva-Ivanova's conjecture concerning the decomposability of square-free solutions to the Yang-Baxter equation, significantly motivated f…

math.RA2025

Central series' and ( $n$ )-isoclinism of skew left braces

Arpan Kanrar, Charlotte Roelants, Manoj K. Yadav

The aim of this article is to advance the knowledge on the theory of skew left braces. We introduce a subclass of skew left braces, which we denote by $I_{n}$ , $n \geq 1$ , s…

math.GR2023

Involutive Yang-Baxter groups never act as Frobenius groups

Arpan Kanrar, Wolfgang Rump

A conjecture of S. Ram\'ırez states that every indecomposable non-degenerate involutive set-theoretic solution to the Yang-Baxter equation with dihedral permutation group of order…

math.GR2023

Cycle matrices: A combinatorial approach to the set-theoretic solutions of the Quantum Yang-Baxter Equation

Arpan Kanrar, Saikat Panja

An $n \times n$ matrix $M = [m_{ij}]$ with $m_{ij} \in U_{n} = {1, 2, \dots, n}$ will be called a cycle matrix if $(U_{n}, \cdot)$ is a cycle set, where $i \cdot j = m_{ij}$ . We study these matr…