# Wide simple Lie algebras

`2019-03-06 10:30:00``2019-03-06 11:30:00``Wide simple Lie algebras``We say that a group G is wide if it contains an element which is not representable as a single commutator of elements of G. Recently it was proven that a finite simple group cannot be wide, thus confirming a conjecture of Ore of 1950's. On the other hand, during the past decades there were discovered several examples of wide infinite simple groups. In a similar vein, we say that a Lie algebra is wide if it contains an element which is not representable as a single Lie bracket. A natural question to ask is whether there exist wide simple Lie algebras. Our goal is to present first examples of such Lie algebras. The simplest example relies on a recent work of Billig and Futorny on Lie algebras of vector fields on smooth affine varieties. This talk is based on a work in progress, joint with Andriy Regeta.``Third floor seminar room (room 201, building 216)``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`We say that a group G is wide if it contains an element which is not representable

as a single commutator of elements of G. Recently it was proven that a finite simple

group cannot be wide, thus confirming a conjecture of Ore of 1950's. On the other hand,

during the past decades there were discovered several examples of wide infinite simple

groups.

In a similar vein, we say that a Lie algebra is wide if it contains an element which is not

representable as a single Lie bracket. A natural question to ask is whether there exist

wide simple Lie algebras. Our goal is to present first examples of such Lie algebras.

The simplest example relies on a recent work of Billig and Futorny on Lie algebras of vector

fields on smooth affine varieties.

This talk is based on a work in progress, joint with Andriy Regeta.

Last Updated Date : 26/01/2019