6 papers
The Köthe conjecture via point modules
B. Greenfeld, B. King, L. Vendramin
We give a short construction refuting the Köthe Conjecture. The construction is based on the point module approach to the problem, introduced by the first-named and second-named au…
Point modules of Nichols algebras over non-abelian groups
B. Greenfeld, L. Vendramin, S. Venkatesh
Nichols algebras are among the most important and mysterious objects in quantum algebra. We continue the systematic program of studying them through their point modules. We study t…
How Many Reflections Make a Dihedral Set Large?
Be'eri Greenfeld, George King, Xiaoxuan Li +1
Given a size- subset of a group , how large can the product set be? We study this question, at several layers of refinement, for the infinite dihedral group. First,…
Complexity and recurrence in infinite words and related structures
Be'eri Greenfeld, Carlos Gustavo Moreira, Efim Zelmanov
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recu…
Modules over Fomin-Kirillov algebras and their subalgebras
Be'eri Greenfeld, Sarah Mathison, Aditya Saini +1
We compute the truncated point schemes of subalgebras of Fomin-Kirillov algebras associated with certain graphs. While Fomin-Kirillov algebras do not admit any truncated point modu…
Gaps and approximations in the space of growth functions
Be'eri Greenfeld
An important problem in combinatorial noncommutative algebra is to characterize the growth functions of finitely generated algebras (equivalently, semigroups, or hereditary languag…