Date:
Thu, 07/07/202210:00-11:00
Location:
The Hebrew University of Jerusalem, Jerusalem
Speaker: Alon Romano (HUJI)
Title: On the identity f(x)=x^n in associative algebras.
Where: Ross 70, Givat Ram campus
When: 11:00-12:00, July 7
ZOOM link: https://huji.zoom.us/j/82812963886?pwd=iQJroz_RADItOD0k0g0leImbmxk9_W.1
Title: On the identity f(x)=x^n in associative algebras.
Where: Ross 70, Givat Ram campus
When: 11:00-12:00, July 7
ZOOM link: https://huji.zoom.us/j/82812963886?pwd=iQJroz_RADItOD0k0g0leImbmxk9_W.1
Abstract:
What can be said about an associative (non-unitary) algebra A, satisfying the identity x^n=0 for every x in A? A famous (yet surprising!) theorem from Nagata and Higman (1956) states that there exists N=N(n) such that A^N=0. However, the exact value of N is an open problem for every n>4.
During this talk, we will present some new results relating to this problem, as well as show how representation theory of the symmetric group S_n can be used to reduce some calculations, suggesting a new horizon for attacking the original problem.