Urban Jezernik

collaborators

6 papers

math.RA2026

Random generation of the special linear Lie algebra over finite fields

Urban Jezernik, Andoni Zozaya

We prove that the special linear Lie algebra $sl_{n} (F_{q})$ over a finite field of characteristic $p$ is generated by two random elements with high probability as…

math.RA2026

Diameter bounds for finite simple Lie algebras

Marco Barbieri, Urban Jezernik, MatevÅ¾ MiÅ¡ÄiÄ

We prove strong and explicit diameter bounds for finite simple Lie algebras, which parallel Babai's conjecture for finite simple groups. Specifically, we show that any nonabelian f…

math.SP2026

Strong convergence of random representations of free products of finite groups

Marco Barbieri, Urban Jezernik

We extend the polynomial method of Chen--Garza-Vargas--Tropp--van Handel and Magee--Puder--van Handel for operator-norm bounds in random permutation models to the setting where tor…

math.RA2025

Random Lie bracket on $sl_{2} (F_{p})$

Urban Jezernik, MatevÅ¾ MiÅ¡ÄiÄ

We study a random walk on the Lie algebra $sl_{2} (F_{p})$ where new elements are produced by randomly applying adjoint operators of two generators. Focusing on the…

math.RT2025

Additive diameters of group representations

Urban Jezernik, Å pela Å penko

We explore the concept of additive diameters in the context of group representations, unifying various noncommutative Waring-type problems. Given a finite-dimensional representatio…

math.RA2025

Two-generation of traceless matrices over finite fields

Omer Cantor, Urban Jezernik, Andoni Zozaya

We prove that the Lie algebra $sl_{n} (F_{q})$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when…